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In this paper, by using the theory of quantum calculus, we introduce a class of combinatorial numbers and polynomials. In particular, the class of q-combinatorial numbers introduced in this work is a q-analogue of the combinatorial numbers recently defined by Simsek [9]. We also construct a formula for the generating functions of these q-combinatorial n umbers in terms of q-exponential functions. Furthermore, applying q-derivative, we analyze some properties of these q-combinatorial numbers and their generating functions. As a result of this analysis, we give a few remarks related to our findings. Finally, we conclude the paper with a brief observation on our results. [ABSTRACT FROM AUTHOR]

This paper deals with different power series expansions of generalized holomorphic (monogenic) functions in the setting of Clifford Analysis. Our main concern are generalized Appell polynomials as a special class of monogenic polynomials which have been introduced in 2006 by two of the authors using several monogenic hypercomplex variables. We clarify the reasons why a particular pair of non-monogenic variables allows to obtain a power series expansion by those generalized Appell polynomials. The approach is based on the differential of a function. Some other monogenic polynomials as well as applications are mentioned. [ABSTRACT FROM AUTHOR]

We revisit a special rational number sequence, introduced by L. Vietoris in 1958 in the study of the positivity of some trigonometric sums and used in other contexts by several authors. The aim of the present paper is to embrace and explore real and hypercomplex analytical methods to obtain generalizations of that rational number sequence, where Jacobi polynomials and generalized Appell polynomials are involved. [ABSTRACT FROM AUTHOR]

The main idea of this paper is to give some identities and applications of the two parametric kinds of Eulerian-type polynomials. By using generating functions and functional equations of these special polynomials, we derive some identities and relations associated with the two parametric kinds of Eulerian-type polynomials, the Hermite polynomials, and well-known combinatorial numbers and polynomials. Moreover, we give a remark on these special polynomials and functions. [ABSTRACT FROM AUTHOR]

Interesting interconnections between Hybrid Fibonacci and Lucas polynomials in two variable and golden ratio are worked out in the present paper. Inter connections are due to close relationship existing between hybrid Lucas and Fibonacci polynomials and the four kinds of Tchebyshev polynomials. In this way, the present paper provides a better interconnecting combinatorial picture of the golden ratio as well as hybrid Fibonacci and Lucas polynomials. [ABSTRACT FROM AUTHOR]

The aim of image compression is to reduce the required bytes efficiently that effectively affected the stored and/or communicated data, based on exploiting the redundancy(s). The techniques classified according either the redundancy removal that impels the lossless and lossy scheme or the way of removing redundancy that impels spatial, transform and hybrid coding. Images are over-burdened with redundancies, where for grayscale images the spatial (interpixel) redundancy embedded between image pixels, while for color images the spectral redundancy between color bands and along the band itself of spatial redundancy base, in addition to coding and psycho-visual redundancies that existed in both types. Today, various acceptable standard image compression techniques available, such as the graphics interchange format (GIF), joint photographic experts group (JPEG), or JPG2 (JPEG-2000), with always need to new compression schemes of high performance. Polynomial coding of the spatial efficient modern image compression techniques still under development where the core involves predictions and differentiation (residual) of modelling base, this paper reviews the main efforts related to compress grayscale and color images using the polynomial coding techniques. [ABSTRACT FROM AUTHOR]

In the present paper we study error estimation by new family of Generalized Bernstein type Polynomial in terms of modulus of continuity. In this paper we obtained new results related to generalizations of Bernstein's approximation theorem using Lebesgue integrable function. The main aim of the present paper, is to extend the result due to Bernstein [1], Lorentz [5] and Voronowskaja [6] for Labesgue integrable functions in L1-norm by polynomial, which is more generalized form. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph of order n. Let Dcve(G, i) be the family of connected vertex-edge dominating sets of G with cardinality i. The polynomial D c v e (G , x) = ∑ i = γ c v e n (G) d c v e (G , i) x i is called the connected vertex-edge domination polynomial of G where dcve(G, i) is the number of vertex-edge dominating sets of G. In this paper, we study some properties of connected vertex-edge domination polynomials of the Fan graph Fn. Also we obtain some properties of Dcve(Fn,x) and their coefficients. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to present some new properties of the classic Weierstrass iterative method for the simultaneous approximation of all zeros of a polynomial. We obtain the new results using the equivalence of the Weierstrass procedure and a recent method for solving the eigenvalue problem of the Frobenius companion matrix. In addition we derive new proofs of some known theoretical properties for the method of Weierstrass. [ABSTRACT FROM AUTHOR]

In this paper the conditional optimization problem is considered for two functions. One of them is to minimize under the restrictions on another one. The measured table values of both functions are approximated by polynomials of the second degree in two arguments. If there is some a priory information, the tables can be reduced, it will make the approximation more accurate, but will make it more dependent on measuring errors. In the paper the reduced area preference criterion is proposed. One example with coolant parameters is considered. [ABSTRACT FROM AUTHOR]

The paper deals with the eigenvalue computation of real symmetric matrices of size three. This problem is usually a part of student exams in the basic linear algebra courses and the solution by the characteristic polynomial belongs to crucial skills of successful graduates. However, in practical applications, e.g., numerical solution of elastoplasticity problems by finite element method, this basic solution process is not applicable and the problem is solved numerically. For instance, Matlab provides the "eig" command for the eigenvalue computation but the sequential calling of this function through all of the integration points can became easily the bottleneck. In our contribution, we provide and examine the vectorized approach of the solution process, which can be easily implemented in any scripting language, such as Matlab or Python. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to give a form of the operator involving the Apostol-Genocchi polynomials of order α. To begin with, we construct the Kantorovich-Szász type generalization of these operators. In addition, we obtain some theorems on convergence and the order of convergence of the operator involving the Apostol-Genocchi polynomials of order α. [ABSTRACT FROM AUTHOR]

In the present paper, we explore some new formulae of fractional calculus, including the general class of polynomials given by Srivastava [5] and the generalized Hurwitz–Lerch zeta function given by Nadeem et al. [11]. The obtained results are in the form of hypergeometric function, which are made with the help of Hadamard product. We have also derived some important special cases from the main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multi-projection methods for solving the mixed type Urysohn integral equation, using Legendre polynomial basis functions. Superconvergence results are obtained for approximate solutions in both infinity and L2-norm. [ABSTRACT FROM AUTHOR]

In this digital era, the amount of sensitive data getting transferred every day is very high, the digitization of all data brought a lot of advantages along with serious security threats. The security standards exist in present scenario provides three basic services such as Confidentiality, Integrity, and Authentication (CIA), the two common types of symmetric and asymmetric algorithms are being used at different levels and capacities. The emerging of new technologies and high computing facilities makes the existing standards vulnerable to different attacks and security threats. There is a need of developing a new set of cryptographic algorithms those are quantum-safe, which means, the arrival of quantum computers can break any sized keywithin a polynomial solvable time, the quantum computers can do prime factorization in realistic time complexities. There are new and smart cryptanalysis emerging to break the existing standards such as Advanced Encryption Standard (AES) and RSA, these algorithms are ruling the cyber world for more than two decades. In this research paper, a new concept of using polynomials to encrypt and decrypt data is proposed, however, the power of polynomials are not fully explored in cryptography, we use Newton Raphson method and its advancements to implement a new cryptography algorithm that is more accurate and faster than existing standards. The proposed algorithm doesn't use any fixed size to avoid cryptanalysis and attacks based on key sizes, the highly intensive computing can break any length of key in realistic time delays, so variable sized key solves this problem in our approach. [ABSTRACT FROM AUTHOR]

The most important aim of this paper is to study some special cases of the open problem for ordinary generating functions (OGFs) for the combinatorial Simsek numbers of the sixth kind given by Simsek in [12]. The other aim is to give some identities and relations, including these numbers and others, via these generating functions. Finally, we present some applications of some special values of these results. [ABSTRACT FROM AUTHOR]

In this paper, we consider two new polynomials, partially degenerate Changhee-Genocchi polynomials and partially degenerate Changhee-Genocchi poynomials of higher-order. We analyzed some properties and formulas of these polynomials. Moreover, we derive multifarious correlations for these polynomials, including Changhee polynomials, Daehee polynomials, Stirling numbers of the first and the second kinds, and partially degenerate Changhee-Genocchi polynomials. [ABSTRACT FROM AUTHOR]

The aim of this paper is to design neural network (NN) for solving the singular perturbation problems of partial differential equations. The modified neuro system (MNS1) using a polynomial of second degree to replace each component in the training set. The foundament of this process is to variation each x in the input vector training set x → = (x1, x2, ..., xn), xj∈[a, b] the polynomial ξ (x) = λ 2 (x 2 + x + 1) , λ ∈(a, b). We were able to determine the appropriate value within a certain range, which has a significant impact on the accuracy of the solution. Our numerical results showed that (MNS1) method is better and more accuracy, of course, the main reason for this point connected with the chosen value of λ. Finally, the method of updating the neural network was clarified through the numerical results, which were compared to traditional methods, and through which we proved the accuracy of the solution and the rapidity of convergence. [ABSTRACT FROM AUTHOR]

The present paper is devoted to derive a generalized Oberhettinger-type integral formula. The derived form of the integral involves a finite product of the Srivastava polynomials with the four-parameter Bessel functions. The outcomes are obtained in terms of the Srivastava and Daoust-type functions. Some of the significant particular cases are also determined. [ABSTRACT FROM AUTHOR]

In this paper, a new technique is formulated to find out the approximate solution for some problems in astrophysics. The methodology that presented in this work is converting the original problem into a system of algebraic equations in the unknown coefficients. For this purpose, the shifted Vieta-Pell polynomials are used for constructing a new variable order operational matrix of differentiation. The collocation method and the constructed operational matrix are utilized at the collocation points for transforming the astrophysics problem into an algebraic system of equations that are solved numerically. In the end, the applicability and accuracy of the suggested method are demonstrated through some numerical applications. In addition, the results are compared with the results of other methods in the literature. [ABSTRACT FROM AUTHOR]

This paper shows the results of a study of the accuracy characteristics, based on the obtained dependence of the specific magnetic resistance on magnetic induction by the method of power polynomials. A comparative assessment of the existing methods of approximation by power polynomials is made and their advantages and disadvantages are revealed. The approximation proposed by the author most accurately reflects the nature of the change in the magnetization curve. Convergence of experimental and calculated curves is established. [ABSTRACT FROM AUTHOR]

The paper considers the issues of creating a system of second-order differential equations for controlling a dynamic object described by a system with an elastic property, alignments which are further transformed into two polynomial controls in matrix form. To solve the problem of synthesizing a control system in a control system, two matrix polynomials are introduced into the control system with unknown parameters that were the transfer function of the controller, the order of which is equal to two, which gives the system astatic properties. To solve this problem, matrix polynomial control is converted to matrix linear control with real coefficients. The results of simulation modeling show that the synthesized system meets the requirements of the object, the proposed device allows you to ensure the stability of the system, gives the properties of astaticism, and the duration of the transition process is determined by the location of the poles of the system and the desired quality indicators. [ABSTRACT FROM AUTHOR]

In the present paper optimal quadrature formula for approximate evaluation of Fourier coefficients is constructed for functions of the space K2(Pm)(0, 1). At the same time explicit formulas for the optimal quadrature formulas are obtained. The obtained formula is exact for the trigonometric functions sin ωx, cos ωx and for polynomials of degree m− 3. [ABSTRACT FROM AUTHOR]

In this paper, certain properties of newly defined generalized hypergeometric polynomials in two variables{Rn (β ;γ ; x, y)} have been derived, namely, recurrence relations of ascending and descending type, ordinarydifferential equation and linear generating function, which are essential to derive generating relations of various types from the group-theoretic method point of view. Furthermore, Laguerre polynomials of single and two variables, Meixner, Gottlieb and Krawtchouk polynomials are deduced as special cases, which arises in mathematical physics and communication engineering. [ABSTRACT FROM AUTHOR]

There are numerous regression models in literature and some of them are simple linear, multiple linear, polynomial, Cubic, Stepwise, Ridge, Lasso, Elastic Net, Negative Binomial, Poisson, Partial, Principal Component Regression etc. Generally regression gives single fit for total data. Splines or piecewise regression gives two or more regression lines for data using knots. In this paper we are fitting trigonometric piecewise regression, Polynomial piecewise regression and cubic piecewise regression for Atmospheric data. Best among these three piecewise models is estimated using R square criteria. [ABSTRACT FROM AUTHOR]

The construction of mechanisms for observing oscillations and their registration is one of the main tasks of radio electronics. In this paper, the geometric principle of constructing an algorithm for observing the state space in the problems of control objects stabilization is considered. The observation system is an oscillatory system with a non-ideal energy source, in which circuits of nonlinear feedbacks are formed between the oscillatory subsystem and the energy source. At present, self- oscillating observers are the most important. An energy source that generates self-oscillations, so that when oscillations in the source are determined, the system being observed goes into a self-oscillating mode of a given amplitude and frequency, it is required to build. In this case, the behavior of the oscillating system affects the dynamic characteristics of the source. The solution of the problem is reduced to the synthesis of stabilizing controls in the phase space of each of the circuits and the synthesis of external controls connecting these circuits to each other. The approach to modeling observers is based on the theory of stable invariant sets. The observation system will provide the property of asymptotic attraction of trajectories to the boundary of the region in the phase space of the observed system. The results of numerical modeling of observer dynamics and stabilization of the executive part of the system are illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of polynomials defined by generating functions of form F(t, x)α ⋅ G(t, α)x. We obtain new properties for those polynomials, which allow to obtain interesting identities. As application, using the results of paper we get the identities for the generalized Bernoulli polynomials. [ABSTRACT FROM AUTHOR]

In this paper, the relevance of searching for computational methods for obtaining polynomials is shown. The authors propose to use a library for Wolfram Mathematica as such computational method. This library automates the method based on compositae of generating functions, which helped to obtain explicit formulas for many polynomials. Also, this method allows us to find the composition, sum and product of polynomials. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made to obtain generating functions for the Chebyshev polynomials Tn (x) (Special ultra spherical polynomials of first kind) using Weisner's group-theoretic method by interpreting 'n' suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn(x) are used as matching-points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly. [ABSTRACT FROM AUTHOR]

The polynomial equations demand different solvability criterion in the p-adic field compared to the real field. This is due to the non-Archimedean and finite properties that been used in the p-adic field. In previous work, the solvability criterion of the cubic equations had been studied in depressed form for case p≥2. However, the proof for case prime p = 2 is not complete. This paper will provide the proof of such a problem. [ABSTRACT FROM AUTHOR]

In this paper ,we study the equivalence relationship between the modulus of continuity and k-functional. also the direct and inverse approximation theorems of unbounded functions by trigonometric polynomials in weighted space Lp,ϑ (X) are considered. [ABSTRACT FROM AUTHOR]

In this paper we consider analytical functions of unbounded type on Banach spaces. We are interested in finding under which conditions a given sequence of polynomials supports entire functions of unbounded type. Some relevant counterexamples are indicated. We show if X is an infinite dimensional Banach space, then H(x) \ Hb(X) can be represented as a union of infinite dimensional linear subspaces (without the origin). [ABSTRACT FROM AUTHOR]

In the paper multiplicative polynomials and analytic functions on Fréchet algebras are investigated. Some connections with homomorphisms on symmetric tensor products of the Fréchet algebras are obtained. A method of constructing of multiplicative G-analytic mapping on Fréchet algebras is proposed. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a simple and undirected graph, which has no isolated vertices. A proper subset D⊂V is called the equality co-neighborhood dominating set of G (ENDS), if ∀ v∈D has equally number of neighborhood vertices in the set V – D. In this paper, by using the new definition (ENDS) the G n − 1 i , is constructed and the recursive formula for den(Gn, i) is obtained. The polynomial D e n (G n , x) = ∑ i = 1 n − 1 d e n (G n , i) x i , (equality co-neighborhood domination polynomial) for some graphs with some properties of this polynomial is determined. [ABSTRACT FROM AUTHOR]

This paper discusses two distinct techniques to locate the inverse of a quintic spline, which gives an appropriate strategy to solve and to decide a technique that offers a surmised response which is exceptionally nearer to the first answer. Two strategies are applied in the derivation of quintic spline, gives the determination of inverse equation for quintic spline. On applying a mathematical model which is applied on both series reversion and polynomial iteration methods, which gives an inverse quintic spline polynomial for certain particular interval. Some random values are applied in both the inverse polynomials methods. It assists with taking a choice that which strategy is smarter to locate the inverse quintic spline. [ABSTRACT FROM AUTHOR]

For a graph G of order n, let D be the edge dominating set. Then D is said to be total edge dominating set of G if the induced subgraph D has no isolated edges. In this paper, we investigated the total edge domination polynomial for the spider graph Sp defined as D t e (S p , x) = | E (S p) | ∑ i=γ t ' (S p) d t e (S p , i) x i , where D t e (S p , i) is the total edge dominating sets of Sp with cardinality i and d t e (S p , i) denotes the number of elements in D t e (S p , i) . Also we calculate some properties of the coefficients of D t e (S p ,x) [ABSTRACT FROM AUTHOR]

In this paper, the stability properties of the predictor-corrector mode are investigated in the case when both the predictor and the corrector are symmetric linear multistep methods of the same order. The stability polynomial of the mode is obtained. Conditions are given under which the stability polynomial has at least one root on the unit circle, which makes it possible to develop a constructive algorithm for determining the stability interval of the mode. The stability of the predictor-corrector mode is investigated for a large class of symmetric methods. We compare accuracy and computational costs of the symmetric methods and the Everhart integrator. [ABSTRACT FROM AUTHOR]

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM). [ABSTRACT FROM AUTHOR]

This work's content has been built on the material created in the first two companion papers on the very newly proposed method named "Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions". Those four companion papers are to appear in this proceedings. This work focuses on the univariate numerical integration of a given univariate function by using SNADE. Almost trivial polynomial integration has been empowered by integrating the SNADE remainder integral. To this end the integral representation of the SNADE remainder has been reformulated in unit hypercubic format. The factor arising in the integrand to multiply the target function's relevant derivative has been separated to appropriate pieces to get weighted integrals under strictly positive multivariate weight functions. Paper emphasizes totally onconceptuality and formulation. Hence we do not present any illustrative implementations here. [ABSTRACT FROM AUTHOR]

Interpolation using Hermite polynomial cubic splines is well known and often used. Here we propose an approximation with the non-polynomial splines with the fourth order of approximation. The splines uses the values of the function and the first derivative of the function in the nodes. We call the approximation as first level approximation because it uses the first derivative of the function. This approximation has the properties of polynomial and trigonometric functions. Here we also have constructed a non-polynomial interpolating spline which has continuous the first and second derivative. This approximation uses the values of the function at the nodes and the values of the first derivative of the function at the ends of the interval [a, b]. Estimates of the approximations are given and the constants included in them are calculated. Numerical examples are given. [ABSTRACT FROM AUTHOR]

Fundamental idea of this paper is to study some properties of the generating functions for Apostol-Genocchi type polynomials by using trigonometric functions. Moreover, by considering these functions, we give some identities and relations including parametric kinds of Apostol-Genocchi type polynomials, the Bernoulli numbers, trigonometric functions involving the tangent numbers and the cotangent numbers. Furthermore, by taking into account the generating and trigonometric functions, we derive some combinatorial sums, formulas and relations which are related to these numbers and polynomials. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze higher-order Peters-type combinatorial numbers and polynomials by means of their generating functions and p-adic integration. By using generating functions we first obtain a combinatorial identity containing not only these numbers and polynomials, but also the Stirling numbers of the first kind, the falling factorial and binomial coefficients. Secondly, by implementation of p-adic integration into the combinatorial sum representation of higher-order Peters-type combinatorial polynomials which includes falling factorial function, we provide both bosonic and fermionic p-adic integral representations of these numbers and polynomials. [ABSTRACT FROM AUTHOR]

We deal with the numerical solution of one-dimensional Poisson equation. Guaranteed a posteriori upper bound based on the hypercircle theorem is derived. Important part of this technique is the reconstruction of the original discrete fluxes such that they belong to H(div). The main aim of this paper is to show that the robustness of the presented reconstruction depends on p1/2 at most, where p is the discretization polynomial degree. The theoretical results are verified by the numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we produced n-points quadrature method which is a Derivative-based Quadrature method on the compact interval [-1,1] with a constant weight function. This n-point Quadrature method looks like as Taylor series and includes up to n - 1 derivatives of a given function. This quadrature rule is the exact result to the polynomials of degree 2n-1 or less by the best values of the points and weights. We will show rules and errors up to n=5 on this paper. [ABSTRACT FROM AUTHOR]

In this paper we submit a new family of general dimension hyperplanes arrangements, that is Shi arrangement of type An-1. Depending on the lattice of arrangement (shi arrangement) we compute the Poincare Polynomial and the characteristic polynomial, and we prove that (Shi arrangement) is not hypersolvable and nor supersolvable. [ABSTRACT FROM AUTHOR]

In this paper, types of Horadam polynomials are used to solve a Mathematical modelling of causing fungal diseases, the main advantage of these polynomials are use it in solving nonlinear ordinary and partial differential equations. The obtained results are compared with the Laplace Adomian decomposition method for epidemiological model to show the efficiency and reliability of the proposed method which can be extended to solve a large variety of ordinary differential equations. Tables are also given to show the variation of the absolute errors for large approximation. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to make use of the Hordam polynomials Hn(x), in order to submit and discuss three new subclasses of the class Σ consisting of holomorphic bi-univalent functions in the open unit disk Δ. For functions belonging to the defined classes, we then derive coefficient bounds and the Fekete-Szegӧ problems. Also, we obtain new special cases for our results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to use a suitable algebraic polynomial that operators in weighted space to compute the degree best algebraic monotone approximation of unbounded in LP,w([−1,1]) space. These proofs include the modulus of smoothness of the second order, which is equivalent to the K-Functional are considered. [ABSTRACT FROM AUTHOR]

Interpolation is a mathematical technique employed for estimating unknown values between data points. This technique assures that the resulting polynomial passes through all data points. One of the most useful interpolation polynomials is the parametric interpolation polynomial. Bézier interpolating surfaces are parametric interpolation polynomials that produce smooth, flexible, and accurate functions. One of the most crucial parts in deriving Bézier interpolating surfaces is to construct control points. However, the control points constructed by most of the existing strategies produce partial smoothness functions with less accurate solutions. In this paper, a new strategy for constructing control points is proposed. This strategy interpolates diagonal data points to construct control points of three-dimensional (3D) datasets. The obtained control points are then employed to derive Bézier interpolating surfaces that preserve stability and smoothness. The newly derived Bézier interpolating surfaces are then applied in colour image upscaling. Not only do the derived Bézier interpolating surfaces produce sharper upscale images, the numerical results show that they also produce more accurate solutions than other existing methods. [ABSTRACT FROM AUTHOR]

Recently, a method known as Cubic Polynomial has been proposed for walking on a flat surface. However, the Cubic Polynomial algorithm has not been tested yet with NAO humanoid robot with single swing leg. In this paper, we study the problem of a swing leg motion (Left Leg) as part of the starter to make the robot walk. The Cubic Polynomial allow the robot to concern itself with the method of computing a trajectory that describes the desired motion of a swing leg in multidimensional space. The method trajectory refers to a time history of position, velocity and acceleration for each degree of freedom. The simulation to test the method is using CoppeliaSim Edu by Coppelia Robotics with 50 seconds time for a swing leg. As a result, the force that captured from the Force Sensitive Resistor (FSR) of the robot will be measured as a stability for the robot. [ABSTRACT FROM AUTHOR]