Search

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations. [ABSTRACT FROM AUTHOR]

In the present paper, the initial value problem for the third order partial differential equation with time delay is studied. The first and second order of accuracy difference schemes for the numerical solution of the third order partial differential equation with time delay are presented. The illustrative numerical results are provided. [ABSTRACT FROM AUTHOR]

The Fourier series, Laplace and Fourier transforms are applicable for the solution of parabolic type involutory differential problem with constant or polynomial coefficients. In the present paper, the first and second order of accuracy difference schemes for the numerical solution of the initial boundary value problem for one dimensional parabolic type involutory partial differential equation are presented. Numerical results are given. [ABSTRACT FROM AUTHOR]

This paper presents a study on the dissemination of information from the source node by establishing information potentials that uses the information gradient descent method. The information gradient is computed by solving the discrete approximation of a partial difference equation. The solution to this equation is the harmonic functions which are also known as harmonic information potentials. Commonly used iterative method for solving partial difference equation to obtain the harmonic information potentials was the classical Jacobi that was found to be too slow when it dealt with large domain. This study proposes faster iterative methods using Gauss-Seidel and Successive Overrelaxation with Red-Black ordering strategy (GS-RB and SOR-RB), as well as Modified Successive Overrelaxation (MSOR) schemes. The experimental results show that the execution time of GS-RB, SOR-RB and MSOR are faster than the existing methods. The advantage of the proposed methods in terms of computational speed is clearly shown with increasingly large domain size. [ABSTRACT FROM AUTHOR]

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach. [ABSTRACT FROM AUTHOR]

A family of symmetric three-stages eight-step embedded (S3SESME) methods with eliminated phase-lag and its derivatives are described in this paper. Since the methods have three stages are belonged to the category of hybrid methods. For the new proposed family of methods we request elimination of the phase-lag and its derivatives. We note here that for this specific family of embedded pairs the phase-lag and the stability analysis are studied on the whole scheme and no on each stage of each scheme. The obtained families of embedded pairs are applied on the approximate solution of the Schrödinger equation and other related problems. The theoretical and numerical achievements show the effectiveness of the new developed embedded pairs. [ABSTRACT FROM AUTHOR]

Embedded predictor-corrector methods with two-stages of prediction and with vanished phase-lag and its derivatives are described in this paper. We give the symbol (EP²CM) since these methods have two-stages of prediction. The first stage of the predictor of the new algorithm is based on the linear eight-step symmetric method of Quinlan-Tremaine [1]. The new scheme is non-linear since has three-stages. These methods can be used on the approximate solution of: 1. initial-value problems (IVPs) with oscillatory solutions, 2. boundary-value problems (IVPs) with oscillatory solutions, 3. orbital problems 4. the Schrödinger equation and related problems. The new presented algorithm belongs to the embedded methods. The numerical and theoretical achievements show the efficiency of the new produced embedded scheme. [ABSTRACT FROM AUTHOR]

Modelling and simulation of thermal processes, based on the principles of classical thermodynamics, requires numerical analysis of partial differential equations of evolution of the parabolic type. This paper demonstrates how the generalized Fourier method can be applied to the development of robust and effective computational algorithms, with the direct application to the design and performance of buildings with controlled energy consumption. [ABSTRACT FROM AUTHOR]

The paper considers the problem of estimating the stress-strain state of a cylindrical pipe section according to measured vertical displacements of a number of cross-sections of the cylinder. The problem is ambiguous, as there are an infinite number of different variants of loading, under the action of which we obtain the same values of displacements at a finite number of the set points of the pipeline. Four variants of such loading from the hard(concentrated load) to soft (continuously distributed according to some rule) are discussed . As a model of a cylindrical pipe section is used the linear theory of thin shells. The method of orthogonal sweep Godunov is used for the numerical solution of the corresponding linear boundary-value problems. [ABSTRACT FROM AUTHOR]

In this paper, the methods of homotopy perturbation sumudu transform is mentioned. Linear and nonlinear Schrödinger equations is solved HPSTM and obtained exact solutions. [ABSTRACT FROM AUTHOR]

The purpose of the talk is the presentation of some recent advances in the numerical solution of differential equations, with special emphasis to reaction-diffusion problems, Hamiltonian problems and ordinary differential equations with discontinuous right-hand side. As a special case, in this short paper we focus on the solution of reaction-diffusion problems by means of special purpose numerical methods particularly adapted to the problem: indeed, following a problem oriented approach, we propose a modified method of lines based on the employ of finite differences shaped on the qualitative behavior of the solutions. Constructive issues and a brief analysis are presented, together with some numerical experiments showing the effectiveness of the approach and a comparison with existing solvers. [ABSTRACT FROM AUTHOR]