The Numerical Solution of Integro-Differential Equations of Parabolic Type

Abstract

Partial integro-differential equations (PIDEs) arise widely in mathematical
models of certain physical phenomena, biological models and chemical
kinetics. The main aim of this study is to investigate numerical solution of the
partial integro-differential equations of parabolic type, as the PIDE contains
two deferent parts, differential part and integral part, we use the fourth order
finite difference method to have accurate results for the differential part, and
composite weighed trapezoidal rule to calculate the integral part. We solve
the integro-differential equations considering the initial-boundary value
problems.