Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations

M Sameeh,A Elsaid

doi:10.1155/2016/7854806

Abstract

An efficient technique for solving parabolic partial integrodifferential equation is presented. This technique is based on Chebyshev polynomials and finite difference method.A priorierror estimate for the proposed technique is deduced. Some examples are presented to illustrate the validity and efficiency of the presented method.

Highlights

Partial integrodifferential equations (PIDEs) are the equations that combine partial differentiation and integration of the unknown function
Chebyshev collocation method is successfully used for solving parabolic partial integrodifferential equation
This method reduced the considered problem into linear system of algebraic equations that can be solved successively to obtain a numerical solution at varied time levels

Summary

Introduction

Partial integrodifferential equations (PIDEs) are the equations that combine partial differentiation and integration of the unknown function. They are used in modeling several phenomena where the effect of memory must be considered. The Chebyshev polynomials are applied through finite difference method to obtain an approximate solution for problems (1) and (2).

Fundamental Relations

Description of Chebyshev Collocation Method

Error Analysis

Numerical Examples

Conclusions