A super accurate shifted Tau method for numerical computation of the Sobolev-type differential equation with nonlocal boundary conditions

In this article, we propose a super accurate numerical scheme to solve the one-dimensional Sobolev type partial differential equation with an initial and two nonlocal integral boundary conditions. Our proposed methods are based on the shifted Standard and shifted Chebyshev Tau method. Firstly, We co...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 236; pp. 683 - 692
Main Authors: Soltanalizadeh, B., Ghehsareh, H. Roohani, Abbasbandy, S.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2014
Subjects:
Boundary conditions
Chebyshev approximation
Computation
Differential equations
Hyperbolic equation
Mathematical models
Nonlocal boundary condition
Partial differential equations
Polynomials
Shifted Chebyshev base
Shifted Standard base
Sobolev-type equation
Tau method
Shifted Chebyshev base
Nonlocal boundary condition
Sobolev-type equation
Shifted Standard base
Tau method
Hyperbolic equation
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this article, we propose a super accurate numerical scheme to solve the one-dimensional Sobolev type partial differential equation with an initial and two nonlocal integral boundary conditions. Our proposed methods are based on the shifted Standard and shifted Chebyshev Tau method. Firstly, We convert the model of partial differential equation to a linear algebraic equation and then we solve this system. Shifted Standard and shifted Chebyshev polynomials are applied for giving the computational results. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. The method is easy to apply and produces very accurate numerical results.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.03.044