Higher-Order Numerical Scheme for the Fractional Heat Equation with Dirichlet and Neumann Boundary Conditions


PRIYA G. S., PRAKASH P., NIETO J. J., Kayar Z.

NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, vol.63, no.6, pp.540-559, 2013 (SCI-Expanded) identifier identifier

Abstract

In this article, we consider a higher-order numerical scheme for the fractional heat equation with Dirichlet and Neumann boundary conditions. By using a fourth-order compact finite-difference scheme for the spatial variable, we transform the fractional heat equation into a system of ordinary fractional differential equations which can be expressed in integral form. Further, the integral equation is transformed into a difference equation by a modified trapezoidal rule. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.