A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation

Author

Bhrawy, Ali H.

Source

Abstract and Applied Analysis

Issue

Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2014-04-30

Country of Publication

Egypt

No. of Pages

10

Main Subjects

Mathematics

Abstract EN

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 P L , n ( x ) P L , 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.

American Psychological Association (APA)

Bhrawy, Ali H.. 2014. A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014409

Modern Language Association (MLA)

Bhrawy, Ali H.. A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1014409

American Medical Association (AMA)

Bhrawy, Ali H.. A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014409

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1014409