Numerical Solution Of System Research Articles

Hybrid Bernstein Block–Pulse functions for solving system of fractional integro-differential equations

ABSTRACTThis paper deals with the numerical solution of system of fractional integro-differential equations. In this work, we approximate the unknown functions based on the hybrid Bernstein Block–Pulse functions, in conjunction with the collocation method. We introduce the Riemann–Liouville fractional integral operator for the hybrid Bernstein Block–Pulse functions. This operator will be approximated by the Gauss quadrature formula with respect to the Legendre weight function and then it is utilized to reduce the solution of the fractional integro-differential equations to a system of algebraic equations. This system can be easily solved by any usual numerical methods. The existence and uniqueness of the solution have been discussed. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Numerical experiments are presented to show the superiority and efficiency of proposed method in comparison with some other well-known methods.

Block steepest descent method based on nonoverlapping domain decomposition, I

AbstractIn the present paper we propose a new iterative method for the numerical solution of system of linear algebraic equations with symmetric positive definite and positive semidefinite matrices arising from the approximation of diffusion equations by the mixed hybrid finite element method on triangular and tetrahedral meshes. The method is based on a combination of the block steepest descent idea and nonoverlapping domain decomposition algorithm. We give the formulation of the method and a simple convergence estimate in the case of regular shaped quasiuniform meshes.

Mixed convection flow over a slender cylinder due to the combined effects of thermal and mass diffusion

This paper deals with the similarity solution of double-diffusive mixed convection flow over a vertical slender cylinder due to the combined effects of thermal and mass diffusion. Local similarity method has been used to transform governing nonlinear partial differential equations into ordinary differential equations. With the help of a set of suitable similarity transformations, the nonlinear coupled partial differential equations governing select phenomena (such as flow, thermal and concentration field) have been reduced to a set of nonlinear coupled ordinary differential equations. Numerical solution of system of nonlinear ordinary differential equations are derived using an implicit finite difference scheme along with quasilinearisation technique. The significant observations of the study are as follows: 1) strong effect of buoyancy parameter λ on the flow and thermal field; 2) strong influence of Prandtl number (Pr) and Sherwood number (Sc) on heat transfer and mass transfer respectively.

Extended source model for diffusive coupling.

Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.

Numerical Solution of System of Fractional Delay Differential Equations Using Polynomial Spline Functions

The aim of this paper is to approximate the solution of system of fractional delay differential equations. Our technique relies on the use of suitable spline functions of polynomial form. We introduce the description of the proposed approximation method. The error analysis and stability of the method are theoretically investigated. Numerical example is given to illustrate the applicability, accuracy and stability of the proposed method.

Multi-Step Iterative Method for Computing the Numerical Solution of Systems of Nonlinear Equations Associated with ODEs

Multi-Step Iterative Method for Computing the Numerical Solution of Systems of Nonlinear Equations Associated with ODEs

Analytic and numerical solutions for systems of fractional Schrödinger equation

In this work, we address the existence and uniqueness of a fractional system involving nonlinear Schrodinger equations. This system of fractional partial differential equations arises in quantum mechanics. It describes how the quantum state of some physical system changes with time. We show that the system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The technique is established as an analytic technique of the fixed point theorem. We suppose that all the functions are analytic in the open unit disk. The fractional differential operator is considered from the point of view of the Riemann-Liouville differential operator. Moreover, a numerical scheme for this solution is calculated.

Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014

Analytical and Numerical Methods for Solving Partial Differential Equations and Integral Equations Arising in Physical Models 2014

Numerical Solution of System of N–Coupled NonlinearSchrödinger Equations via Two Variants of the MeshlessLocal Petrov–Galerkin (MLPG) Method

Numerical Solution of System of N–Coupled NonlinearSchrödinger Equations via Two Variants of the MeshlessLocal Petrov–Galerkin (MLPG) Method

Numerical solution of system of two Nonlinear Volterra Integral equations

In this paper, using the implicit trapezoidal rule in conjunction with Newton's method to solve nonlinear system.We have used a Maple 17 program to solve the System of two nonlinear Volterra integral equations. Finally, several illustrative examples are presented to show the effectiveness and accuracy of this method.

Chebyshev polynomial solution of the system of Cauchy-type singular integral equations of the first kind

This paper presents a Chebyshev series method for the numerical solutions of system of the first kind Cauchy type singular integral equation SIE. The Chebyshev polynomials of the second kind with t...

Numerical Solution for IVP in Volterra Type Linear Integrodifferential Equations System

A method is proposed to determine the numerical solution of system of linear Volterra integrodifferential equations (IDEs) by using Bezier curves. The Bezier curves are chosen as piecewise polynomials of degreen, and Bezier curves are determined on[t0, tf ]by n+1control points. The efficiency and applicability of the presented method are illustrated by some numerical examples.

Chebyshev polynomial solution of the system of Cauchy-type singular integral equations of the first kind

This paper presents a Chebyshev series method for the numerical solutions of system of the first kind Cauchy type singular integral equation (SIE). The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density functions. It is shown that the numerical solution of system of characteristic SIEs is identical to the exact solution when the force functions are cubic functions.

Preservation of stability type of difference schemes when solving stiff differential algebraic equations

Implicit methods applied to the numerical solution of systems of ordinary differential equations (ODEs) with an identically singular matrix multiplying the derivative of the sought-for vector-function are considered. The effects produced by losing L-stability of a classical implicit Euler scheme when solving such stiff systems are discussed.

Numerical Solutions of Systems of High-Order Linear Differential-Difference Equations with Bessel Polynomial Bases

Abstract In this paper, a numerical matrix method, which is based on collocation points, is presented for the approximate solution of a system of high-order linear differential-difference equations with variable coefficients under the mixed conditions in terms of Bessel polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB v7.6.0 (R2008a).

An Analytic Algorithm for Solving System of Fractional Differential Equations

In this article, the variational iteration method has been used to give an analytic algorithm to obtain approximate numerical solutions of system of fractional differential equations modeling some problems in nonlinear chemical reaction, two dimensional heat like equations, free fall under gravity and stiff system of differential equations. Some numerical examples are given to illustrate the simplicity and accuracy of the algorithm.

Multidimensional parametrization and numerical solution of systems of nonlinear equations

The numerical solution of a system of nonlinear algebraic or transcendental equations is examined within the framework of the parameter continuation method. An earlier result of the author according to which the best parameters should be sought in the tangent space of the solution set of this system is now refined to show that the directions of the eigenvectors of a certain linear self-adjoint operator should be used for finding these parameters. These directions correspond to the extremal values of the quadratic form associated with the above operator. The parametric approximation of curves and surfaces is considered.

Numerical method of lines for parabolic functional differential equations

Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the numerical method of lines are given. An explicit Euler method is proposed for the numerical solution of systems thus obtained. This leads to difference scheme for the original problem. A complete convergence analysis for the method is given.

Numerical solution of system of Volterra integral equations using Bernstein polynomials

Numerical solution of system of Volterra integral equations using Bernstein polynomials

An efficient numerical solution for system of second order robot arm problem

The aim of this paper is focused on providing numerical solutions for system of second order robot arm problem using the RK-eight stage seventh order limiting formulas. The parameters governing the arm model of a robot control problem have also been discussed through RK-eight stage seventh order limiting algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. Based on the numerical results, a thorough comparison is carried out between the numerical algorithms. It is observed that RK-eight stage seventh order limiting algorithm is accurate, efficient compared with RK fifth order algorithm and RK-sixth order algorithms.