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