Numerical Solution Of Partial Integro-Differential Equation Using Legendre Multi Wavelets

Abstract

It is very important to state the initial assumptions for the description of physical phenomenon in the case of partial integro-differential equation. The parabolic equations and boundary conditions can be used to define the time-dependent diffusion process. The integro-differential equation is the combination of integration and derivatives. It is part of the technology, which includes science and engineering. Various models that cover the area of science and engineering are available. Moreover, variable techniques are accessible to solve the integro-differential equations. Numerical method is an important way to solve the challenges in the field of science and industry. To improve efficiency, the companies were working on computer simulation. For reliability, flexibility, and inexpensiveness, the numerical methods are preferred. Linear Legendre multi wavelets form a collocated method based on the numerical solution of one-dimensional parabolic partial integro-differential equation of diffusion type. In this study, we aim to study the diffusion method of numerical solution for the integro-partial differential equation. The diffusion method, its basic concept, and other methods used to solve integro-partial differential equations are also studied in detail. The proposed numerical method is useful to different benchmark problems and provides efficient, accurate, and robust results.