Abstract
Block methods for the finite difference solution of linear one dimensional parabolic partial differential equations are considered. These schemes use two linear multistep formulae which, when applied simultaneously, advance the numerical solution by two time steps. No special starting procedure is required for their implementation. By careful choice of the coefficients in these formulae, all of the block methods derived in this paper are unconditionally stable and have high order accuracy. In addition, some of these schemes are suitable for problems involving a discontinuity between the initial and boundary conditions. The results of numerical experiments on two test problems are presented.
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