A new Legendre collocation method for solving a two-dimensional fractional diffusion equation
type: Item
instance of: scholarly article
title: A new Legendre collocation method for solving a two-dimensional fractional diffusion equation
zbMATH Open document ID: 1468.65161
DOI: 10.1155/2014/636191
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: 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 \(P_{L, n}(x) P_{L, m}(y)\), 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.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 7022794
zbMATH Keywords: spectral shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method
zbMATH Keywords: two-dimensional initial-boundary fractional diffusion equations
zbMATH Keywords: variable coefficients
author: A. H. Bhrawy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/636191
OpenAlex ID: W2145798813
Wikidata QID: Q59040252
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description: scientific article; zbMATH DE number 7022794