Preconditioned WR–LMF-based method for ODE systems
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摘要
The waveform relaxation (WR) method was developed as an iterative method for solving large systems of ordinary differential equations (ODEs). In each WR iteration, we are required to solve a system of ODEs. We then introduce the boundary value method (BVM) which is a relatively new method based on the linear multistep formulae to solve ODEs. In particular, we apply the generalized minimal residual method with the Strang-type block-circulant preconditioner for solving linear systems arising from the application of BVMs to each WR iteration. It is demonstrated that these techniques are very effective in speeding up the convergence rate of the resulting iterative processes. Numerical experiments are presented to illustrate the effectiveness of our methods.
论文关键词:15A18,65F10,65F15,65L05,65N22,ODE,WR method,BVM,GMRES method,Block-circulant preconditioner
论文评审过程:Received 13 September 2001, Revised 2 May 2003, Available online 19 November 2003.
论文官网地址:https://doi.org/10.1016/j.cam.2003.08.034