An Approximate Solution of the Space Fractional-Order Heat Equation by the Non-Polynomial Spline Functions

Nabaa N.  Hasan; Omar H.  Salim

doi:10.24996/ijs.2021.62.7.20

Authors

Nabaa N. Hasan Department of Mathematics, College of Science, University of Mustansiriyah, Baghdad, Iraq
Omar H. Salim Department of Mathematics, College of Science, University of Mustansiriyah, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2021.62.7.20

Keywords:

Caputo derivative, non-polynomial spline, tensor product, fractional heat equation

Abstract

The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.