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


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

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

  • Publication Type: Article / Article
  • Volume: 63 Issue: 6
  • Publication Date: 2013
  • Doi Number: 10.1080/10407790.2013.778719
  • Title of Journal : NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
  • Page Numbers: pp.540-559

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.