Approximation of Solution of Time Fractional Order Three-Dimensional Heat Conduction Problems with Jacobi Polynomials

Abstract

In this paper, we extend the idea of pseudo spectral method to approximate solution of time fractional order three-dimensional heat conduction equations on a cubic domain. We study shifted Jacobi polynomials and provide a simple scheme to approximate function of multi variables in terms of these polynomials. We develop new operational matrices for arbitrary order integrations as well as for arbitrary order derivatives. Based on these new matrices, we develop simple technique to obtain numerical solution of fractional order heat conduction equations. The new scheme is simple and can be easily simulated with any computational software. We develop codes for our results using MatLab. Theresults are displayed graphically.