Numerical Solution of Partial Integrodifferential Equations of Diffusion Type

Imran Aziz,Imran Khan

doi:10.1155/2017/2853679

Abstract

A collocation method based on linear Legendre multiwavelets is developed for numerical solution of one-dimensional parabolic partial integrodifferential equations of diffusion type. Such equations have numerous applications in many problems in the applied sciences to model dynamical systems. The proposed numerical method is validated by applying it to various benchmark problems from the existing literature. The numerical results confirm the accuracy, efficiency, and robustness of the proposed method.

Highlights

In some fields such as nuclear reactor dynamics and thermoelasticity we need to reflect the effect of the memory of the systems in model
In order to incorporate the memory effect in such systems, an integral term in the basic partial differential equation is introduced and this leads to a partial integrodifferential equation
The applications of partial integrodifferential equations can be found in financial mathematics [1], biological models, chemical kinetic, aerospace systems, control theory of financial mathematics, and industrial mathematics [2]

Summary

Introduction

In some fields such as nuclear reactor dynamics and thermoelasticity we need to reflect the effect of the memory of the systems in model. We consider one-dimensional partial integrodifferential equation of diffusion type which is given as follows:. Wavelets have been used for numerical solutions of integral equations [19], integrodifferential equations [20], fractional diffusion-wave equation [21], ordinary differential equations [22], and partial differential equations [23]. These methods employ various types of wavelets, which include Daubechies [24], Battle-Lemarie [25], and Haar wavelet [26,27,28].

The Linear Legendre Multiwavelets

Numerical Procedure

Numerical Experiments

Conclusion