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

• 作者: Ahmed A. Mirza Jan Scheffel
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Initial-Value Problem Multiple TIME Scales Time-Spectral SPECTRAL METHOD WEIGHTED RESIDUAL METHOD Subdomains Domain Decomposition
• 年，卷（期）: 2012,（2）
• 页码范围: 72-81
• 页数: 10页
• 分类号: O1

摘要

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.