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Compact finite difference method for the fractional diffusion equation

โœ Scribed by Mingrong Cui

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
606 KB
Volume
228
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

High-order compact finite difference scheme for solving one-dimensional fractional diffusion equation is considered in this paper. After approximating the second-order derivative with respect to space by the compact finite difference, we use the Grรผnwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme. We analyze the local truncation error and discuss the stability using the Fourier method, then we prove that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.

๐Ÿ“œ SIMILAR VOLUMES

Implicit finite difference approximation
Implicit finite difference approximation for time fractional diffusion equations
โœ Diego A. Murio ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 509 KB

Time fractional diffusion equations are used when attempting to describe transport processes with long memory where the rate of diffusion is inconsistent with the classical Brownian motion model. In this paper we develop an implicit unconditionally stable numerical method to solve the one-dimensiona