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Radial basis function (RBF) methods are used widely to solve partial differential equations (PDE). RBF methods have been applied to various diverse fields due to their mesh free characteristics, easy to implement nature and dimensional independence. These methods have been actively developed over the years from global to local approximation and then to hybrid approach. In this paper, various RBF methods are discussed for the solution of option pricing problems arising in finance. Since the price of option can be evaluated as the solution of Black-Scholes equation hence this paper presents review of the RBF methods for various price option problems such as American option, European option and Asian option. [ABSTRACT FROM AUTHOR]

In this paper, by using the theory of strongly continuous cosine family and Schauder's fixed point theorem, we study the approximate controllability of second order semilinear delay control systems. As application, an example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an analytical approximation for Volterra's model for population growth of a species in a closed system by using differential transformation method (DTM). This method is one of the approximate methods which can be easily applied to many linear and nonlinear problems and is capable of reducing the size of computational work. The numerical solutions are obtained by combining DTM and Padc technique. The approximate solutions are shown graphically. [ABSTRACT FROM AUTHOR]

Main aim of present paper is to survey results on multiplicative perturbation of generators of continuous and analytic semi-groups in Hilbert and Banach spaces. Few open problems in that direction are suggested.We as well mention a partial integro-differential equation of age dependent population dynamics, which leads to a problem in multiplicative perturbation of generators of analytic semi-group. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of approximate controllability of random impulsive semilinear control system under a sufficient condition with non-densely defined system. Finally, eximples are given to illustrate the applications of the abstract results. [ABSTRACT FROM AUTHOR]

In this paper, the Natural transform decomposition method (NTDM) which has been constructed by combining Natural transform method (NTM) and Adomian decomposition method (ADM) has been proposed. This algorithm has been applied to obtain the approximate solutions for the modified Camassa-Holm equation (mCHE) and modified Degasperis-Procesi equation (mDPE). Then, two and three dimensional surfaces have been drawn by using Wolfram Mathematica 9. A table including numerical results between approximate solutions which are obtained by using NTDM in this paper and approximate solutions which have already founded by the help of using VIM by Jafari H. et al. with the same values of parameters has been formed for mCHE and mDPE. [ABSTRACT FROM AUTHOR]

In this paper, we compute approximate solutions to systems of nonlinear PDEs using the Reduced Differential Transform Method (RDTM). We examine this method to obtain approximate numerical solutions for four different types of systems of nonlinear partial differential equations, such as the homogeneous KdV equation of the third order types (I) and (II), coupled Zakharov-Kuznetsov system and the coupled Burgers equation. The theoretical analysis of the RDTM is investigated for these systems of equations and is calculated in the form of power series with easily computable terms. Illustrative examples will be presented to support the proposed method. The obtained results are in a good agreement with the exact solutions. This method reduces significantly the numerical computations compared with the existing methods such as the perturbation technique, differential transform method (DTM) and the Adomian decomposition method (ADM). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define the notions of nano strong semi-closed set, nano strong semi-continuity and nano contra strong semi-continuity in nano topological spaces and discuss some of their properties. Also, the notion of NC-set, Nic-set, ND(c; s)-set, ND(c; p)- set, ND(c; ps)-set, ND(c;α)-set and nano strong B-set are introduced and investigated. Further we define, nanoC-continuous, nano A-continuous, nano ic-continuous, nano strongly B-continuous, nano weakly-continuous, nano weak*-continuous, ND(c; p)-continuous, ND(c; s)-continuous, ND(c; ps)- continuous and ND(c;α)-continuous and study the relationships between them and other existing continuities. Further, we have given an appropriate examples to understand the abstract concept clearly. [ABSTRACT FROM AUTHOR]

In the present paper, we propose a two-step modified Natural decomposition method to determine the approximate closed form solutions or rather exact solutions for the nonlinear Klein- Gordon equations if exist. The method is based upon coupling the modified version of the Adomian decomposition method byWazwaz and the Natural transform method. Amazingly, the proposed method gives exact solutions only in two iterations for different nonlinear Klein-Gordon equations with quadratic nonlinearity considered as test problems. [ABSTRACT FROM AUTHOR]

This paper aims at bringing a new point of view to binary products series via Tridiag- onal Kernel Enhanced Multivariance Products Representation (TKEMPR). For this purpose a new version of TKEMPR has been developed such that each additive term of binary products series is represented using bivariate EMPR by starting with appropriate weight functions, and, left and right support functions. Hence we call it "Overlapped Square Blocks Tridiagonal Enhanced Multivariance Products Representation (OSBTKEMPR)". The basic goal of OSBTKEMPR is not to get an efficient approximation scheme since its own structure, as a matter of fact, is based on truncated terms. The main purpose is to reveal the connections between the binary product series and OSBTKEMPR, and then, achieve certain practicalities. [ABSTRACT FROM AUTHOR]

The general expression of the Fluctuationlessness Theorem states that the matrix repre-sentation of an algebraic operator which multiplies its argument by a scalar univariate function, is identical to the image of the independant variable's matrix representation over the same subspace via the same basis set, under that univariate function, when the fluctuation terms are ignored. Just by us-ing this basic idea, function approximation or numerical quadratures can be constructed. Furthermore this principle applied on the remainder term of a Taylor expansion a highly versatile approximation can be obtained. This review article is just about this approximation aspect of the Fluctuationlessness Theorem. [ABSTRACT FROM AUTHOR]

This is a study of the well-posedness and asymptotic stability of a "degenerately damped" PDE that models a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the dissipation. It is shown that the resulting dynamical system has strictly monotonically decreasing energy and uniformly decaying lower-order norms of the solutions, however, it is not uniformly stable on the associated finite-energy space. These theoretical findings were motivated by numerical simulations of this model using an FEM scheme and successive approximations. A description of the numerical approach and sample plots of energy decay are supplied. In addition, for certain initial data the solution can be determined in closed form up to a dissipative nonlinear ordinary differential equation. These special solutions can be used to assess the accuracy of the numerical examples. [ABSTRACT FROM AUTHOR]

A number of models of the real mechanical system nonlinear dynamics approximations are presented. These models, at the same time, present corresponding models of heavy mass particles nonlinear dynamics along rotating circle about a fixed vertical as well as skew positioned axis, with constant angular velocity. In the case of circle rotation around vertical axis with constant angular velocity, it is shown that constant weight force of heavy mass particle, in the ideal constraint, and also kinematic constraint, with constant angular velocity of circle rotation about vertical axis, along which heavy mass particle moves, are sources and causes of nonlinear terms in differential equations of it's dynamics. In the case of circle rotation about skew positioned axis with constant angular velocity, it is shown that constant weight force of heavy mass particle, in the ideal constraint, and also kinematic constraint, with constant angular velocity of circle rotation about skew positioned axis, along which heavy mass particle moves, are sources and causes not only of appearance of nonlinear terms in differential equations of it's dynamics, but also of terms depending explicitly on time. Linearizations and linear and nonlinear approximations of corresponding differential equations about stationary points (stationary regimes) are obtained. Analysis of stability and nostability of system nonlinear dynamics around stationary points (stationary regimes) as well as around relative equilibrium positions of heavy mass particle at circle is presented. It is pointed out that in the phase portraits, a trigger of coupled singularities appears which is a source and cause of possible appearance of chaotic like regimes excited by pure periodical external excitations applied to the mass particle. Also, reasons for investigating the character of local properties of linear as well as nonlinear dynamics around singular points are presented. [ABSTRACT FROM AUTHOR]

We present a local convergence analysis for eighth-order variants of Newton's method in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [7]-[11], [20] using hypotheses up to the seventh derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study. [ABSTRACT FROM AUTHOR]