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arXiv · 1712.05185

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

Vladimir Gordin·Evgenii Tsymbalov
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Abstract

The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-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 difference scheme and then Newton -- Raphson iterations, which are implemented by the double-sweep method. Numerical experiments confirm the 4-th order of an algorithm. The Richardson extrapolation improves it up to the 6-th order.

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Vladimir Gordin, Evgenii Tsymbalov. 2017-12-14. Compact difference schemes for weakly-nonlinear parabolic and Schrodinger-type equations and systems. https://arxiv.org/abs/1712.05185

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