Preconditioned WR-LMF-based method for ODE systems. (Q1421243)

For solving a large system of ordinary differential equations, the waveform relaxation (WR) method was developed, as an iterative method. In each WR iteration, it is required to solve an system of ordinary differential equations (ODEs). Then, for this system the authors apply the boundary value method (BVM), a new linear multistep method. For solving linear system arising from BVM method, the generalized minimal residual method with Strang-type block-circulant preconditioner, is applied. It is proved that these techniques lead to a convergent iterative process. Two numerical examples are performed.