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

Atıf İçin Kopyala

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

NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, cilt.63, sa.6, ss.540-559, 2013 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 63 Sayı: 6
Basım Tarihi: 2013
Doi Numarası: 10.1080/10407790.2013.778719
Dergi Adı: NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.540-559
Orta Doğu Teknik Üniversitesi Adresli: Hayır

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.