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

Priya, G.; Prakash, P.; Nieto, J.; Kayar, Z.

doi:10.1080/10407790.2013.778719

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

Copy For Citation

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)

Publication Type: Article / Article
Volume: 63 Issue: 6
Publication Date: 2013
Doi Number: 10.1080/10407790.2013.778719
Journal Name: NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.540-559
Middle East Technical University Affiliated: No

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.