Time-spectral Solution of Initial-Value Problems
2011 (English)In: Partial Differential Equations: Theory, Analysis and Applications / [ed] Christopher L. Jang, New York: Nova Science Publishers, Inc., 2011, 1, 1-49 p.Chapter in book (Refereed)
A generalized fully spectral weighted residual method (GWRM) for solution of initial value partial differential equations is presented. For all temporal, spatial and physical parameter domains, the solution is represented by Chebyshev series, enabling global semi-analytical solutions. The method avoids time step limitations. The spectral coefficients are determined by iterative solution of a system of algebraic equations, for which a globally convergent root solver has been developed. Accuracy and efficiency are controlled by the number of included Chebyshev modes and by the use of temporal and spatial subdomains. Example applications include the diffusion, Burger and forced wave equations as well as a system of ideal magnetohydrodynamic (MHD) equations. A stiff ordinary differential equation introduces the method. Comparisons with the explicit Lax-Wendroff and implicit Crank-Nicolson finite difference methods show that the method is accurate and efficient. Potential applications of the GWRM are, for example, advanced initial value problems in fluid mechanics and MHD.
Place, publisher, year, edition, pages
New York: Nova Science Publishers, Inc., 2011, 1. 1-49 p.
IdentifiersURN: urn:nbn:se:kth:diva-76035ISBN: 978-1-61122-858-8OAI: oai:DiVA.org:kth-76035DiVA: diva2:490674
QC 201202072012-02-062012-02-062016-06-01Bibliographically approved