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 Legen...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/636191 |
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| Summary: | 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 PL,n(x)PL,m(y), 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. |
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| ISSN: | 1085-3375 1687-0409 |