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r-Modified Crank-Nicholson difference scheme for fractional parabolic PDE

Allaberen Ashyralyev12 and Zafer Cakir3*

Author Affiliations

1 Department of Mathematics, Fatih University, Istanbul, Turkey

2 Department of Mathematics, ITTU, Ashgabat, Turkmenistan

3 Department of Mathematical Engineering, Gumushane University, Gumushane, Turkey

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Boundary Value Problems 2014, 2014:76  doi:10.1186/1687-2770-2014-76

Published: 31 March 2014


The second order of accuracy stable difference scheme for the numerical solution of the mixed problem for the fractional parabolic equation are presented using by r-modified Crank-Nicholson difference scheme. Stability estimate for the solution of this difference scheme is obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional parabolic partial differential equations. Numerical results for this scheme and the Crank-Nicholson scheme are compared in test examples.