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, cilt.63, ss.540-559, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 63 Konu: 6
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1080/10407790.2013.778719
  • Dergi Adı: NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
  • Sayfa Sayıları: ss.540-559

Özet

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.