Time-Spectral Solution of Initial-Value Problems—Subdomain Approach

Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analyt...

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Bibliographic Details
Published in:American journal of computational mathematics 2012, Vol.2 (2), p.72-81
Main Authors: Scheffel, Jan, Mirza, Ahmed A.
Format: Article
Language:English
Subjects:
Algebra
Computational efficiency
domain decomposition
initial-value problem
Mathematical analysis
Mathematical models
Nonlinearity
Polynomials
spectral method
Spectral methods
subdomains
Temporal logic
time-spectral
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Summary:Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.
ISSN:2161-1203
2161-1211
2161-1211
DOI:10.4236/ajcm.2012.22010