Iterated Splitting Method of High Order for Time-Dependent Partial Differential Equations
P.J. van der Houwen · SIAM Journal on Numerical Analysis · 1984
Nonlinear Chebyshev iteration is applied for solving the implicit relations which arise when an implicit linear multistep method is used in order to integrate semi-discrete initial value problems for partial differential equations. The approximate inverse occurring in the defect correction process is obtained by employing splitting methods. In order to accelerate convergence the Chebyshev iteration process is tuned in such a way that the lower frequencies in the iteration error are strongly damped without using a large number of iterations. For moderate accuracies this method is already markedly more efficient then conventional ADI methods.