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Working paper

Compact di fference schemes for weakly-nonlinear parabolic and Schrodinger-type equations and systems

Gordin V. A., Tsymbalov E. A.
The implicit compact fi nite-diff erence scheme was developed for evolutionary partial di fferential parabolic and Schrodinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we need to solve a non-linear system. We use for this step a simple explicit diff erence scheme and then Newton - Raphson iterations, which are implemented by the double-sweep method. Numerical experiments con firm the 4-th order of an algorithm. The Richardson extrapolation improves it up to the 6-th order.