Circulant preconditioned WR-BVM methods for ODE systems. (Q1421226)

The numerical solution of a system of linear ordinary differential equations (ODEs) by waveform relaxation (WR) iterations together with the boundary value method (BVM) is discussed. For discretization of the system the BVM methods are used in each WR iteration. For the new linear system arising from the application of BVM methods, the generalized minimal residual method, with block-circulant preconditioners is applied. These techniques lead to a convergent iterative process as is proved. Numerical tests confirm the effectivness of the proposed methods.