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

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DOI: 10.4236/ajcm.2012.22010    4,656 Downloads   7,623 Views   Citations

ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Scheffel and A. Mirza, "Time-Spectral Solution of Initial-Value Problems—Subdomain Approach," American Journal of Computational Mathematics, Vol. 2 No. 2, 2012, pp. 72-81. doi: 10.4236/ajcm.2012.22010.

References

[1] J. Scheffel, “A Spectral Method in Time for Initial-Value Problems”, American Journal of Computational Mathe- matics, 2012.
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[5] J. Scheffel and C. H?kansson, “Solution of Systems of Non-Linear Equations—A Semi-Implicit Approach”, Applied Numerical Mathematics, Vol. 59, No. 10, 2009, pp. 2430-2443. doi:10.1016/j.apnum.2009.05.002
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