Explicit difference method for solving the two-dimensional two-sided fractional diffusion equation in the shifted grunwald estimate form

Authors

  • N.M. T. Luma Department of Mathematics, College of Education for Pure Science / Ibn Al-Haitham Baghdad University, Iraq
  • I. G. Iman Department of Mathematics, College of Education for Pure Science / Ibn Al-Haitham Baghdad University, Iraq

Keywords:

Fractional derivative,Explicit euler method,Fractional diffusion equation,Stability,Convergence

Abstract

In this paper, weintroduce and discuss an algorithm for the numerical solution oftwo-dimensional two-sided fractional diffusion equation. The algorithm for thenumerical solution of this equation is based on explicit finite difference approximation.Consistency, conditional stability, and convergence of the fractional ordernumerical method are described. Finally, numerical example is provided to showthat the numerical method for solving  this equation   is an effectivesolution method.

References

Isaacson, E., Keller, H.B., 1966. Analysis of Numerical Methods. Wiley. New York.

Joaquín, Q.M., Santos, B.Y., 2011. An Explicit Difference Method for Solving Fractional Diffusion and Diffusion-Wave Equations in the Caputo Form. J. Comput. Nonlinear Dynam., APRIL, Vol.6 .

Lin, R., Liu, F., 2004. Analysis of Fractional- Order Numerical Method for the Fractional Relaxation Equation. J. comp. Appl. Math., Vol.91, PP. 198-210.

Liu, Q., Liu, F., Turner, I., Anh, V., 2009. Numerical simulation for the 3D seepage fllow with fractional derivatives in porous media. IMA J. Appl. Math., Vol.74, PP.201-229.

Meerschaert, M.M., Scheffler, H.P., Tadjeran, C., 2006. Finite difference methods for two dimensional fractional dispersion equation. J. Comput. Phys., Vol. 211, PP. 249–261.

Meerschaert, M.M., Tadjeran, C., 2007. A second-order accurate numerical method for the two-dimensional fractional diffusion equation. J. Comput. Phys., Vol. 220, PP. 813–823.

Meerschaert, M.M., Tadjeran, C., 2004. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math., Vol.172, PP. 65–77.

Meerschaert, M.M., Tadjeran, C., 2006. Finite difference approximations for two-sided space fractional partial differential equations. Appl. Numer. Math., Vol. 56, No. 1, PP. 80–90.

Miller, K., Ross, B., 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley and Sons, New York.

Morton, K.W., Mayers, D.F., 1994. Numerical Solution of Partial Differential Equations. Camb. Univ. Press. Camb., UK.

Podlubny, I., 1999. Fractional Differential Equations. Academic Press, New York.

Roop, J.P., 2005. Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R2. J. Comput. Appl. Math.,

Smith, D.D., Numerical Solution of Parial Differential Equations: Finite Difference Methods. Oxf. Appl. Math. Comput. Sci. Series, Oxford University.

Varga, R., 1962. Matrix Iterative Analysis. Prentice Hall, New Jersey.

Yuste, S.B., Acedo, L., 2005. On an Explicit Finite Difference Method for Fractional Diffusion Equations. SIAM. Soc. Ind. Appl. Math. J. Numer. Anal., 42, PP. 1862–1874.

Downloads

Published

2013-09-29

How to Cite

T. Luma, N., & G. Iman, I. (2013). Explicit difference method for solving the two-dimensional two-sided fractional diffusion equation in the shifted grunwald estimate form. Scientific Journal of Pure and Applied Sciences, 2(9), 314-322. Retrieved from http://sjournals.com/index.php/sjpas/article/view/965

Issue

Vol. 2 No. 9 (2013): September

Section

Mathematics

License

Copyright (c) 2013 N.M. T. Luma, I. G. Iman

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.