Preconditioned WR-LMF-based method for ODE systems

Authors:
Xiao-qing Jin;Vai-kuong Sin;Li-li Song
Affiliations:
Faculty of Science and Technology, University of Macau, C. Postal 3001, Macau, China;Faculty of Science and Technology, University of Macau, C. Postal 3001, Macau, China;Faculty of Science and Technology, University of Macau, C. Postal 3001, Macau, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

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.