Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 636191, 10 pages.
A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation
A new spectral shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method is developed and analyzed to solve a class of two-dimensional initial-boundary fractional diffusion equations with variable coefficients. The method depends basically on the fact that an expansion in a series of shifted Legendre polynomials , for the function and its space-fractional derivatives occurring in the partial fractional differential equation (PFDE), is assumed; the expansion coefficients are then determined by reducing the PFDE with its boundary and initial conditions to a system of ordinary differential equations (SODEs) for these coefficients. This system may be solved numerically by using the fourth-order implicit Runge-Kutta (IRK) method. This method, in contrast to common finite-difference and finite-element methods, has the exponential rate of convergence for the two spatial discretizations. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 636191, 10 pages.
First available in Project Euclid: 6 October 2014
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Bhrawy, A. H. A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 636191, 10 pages. doi:10.1155/2014/636191. https://projecteuclid.org/euclid.aaa/1412607137