Finite integration method using chebyshev polynomials for solving time-dependent linear partial differential equations and linear fractional order differential equations

Abstract

In this thesis, we devise numerical algorithms base on the finite integration method (FIM) using Chebyshev polynomial to find numerical solutions of time-dependent linear partial differential equations and linear fractional order differential equations. The results show that for time-dependent linear partial differential equations, our algorithm gives a lot better accuracy than the traditional FIMs. Several examples illustrate that our algorithm for linear fractional order differential equations gives good approximate solution as well.