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.

Initial-Value Problem; Multiple Time Scales; Time-Spectral; Spectral Method; Weighted Residual Method; Subdomains; Domain Decomposition

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.