A numerical solution of variable order diffusion and wave equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Basic Sciences, Bozorgmehr University of Qaenat, Qaenat, Iran.

2 Department of Mathematics, University of Mazandaran, Babolsar, Iran. Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa.

3 Department of Mathematics, University of Mazandaran, Babolsar, Iran.

Abstract

In this work, we consider variable order difusion and wave equations. The derivative is described in the Caputo sence of variable order. We use the Genocchi polynomials as basic functions and obtain operational matrices via these polynomials. These matrices and collocation method help us to convert variable order diffusion and wave equations to an algebraic system. Some examples are given to show the validity of the presented method.

Keywords