An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions

The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equat...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (1)
Main Authors: Tohidi, E., Kılıçman, A.
Format: Article
Language:English
Subjects:
Accuracy
Algebra
Algorithms
Approximation
Boundary conditions
Collocation methods
Efficiency
Finite element analysis
Mathematical analysis
Mathematical models
Mathematical problems
Mathematics
Methods
Parabolic differential equations
Partial differential equations
Spectra
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Summary:The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs) subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/369029