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

2017/12/14 by Gordin, Vladimir, Tsymbalov, Evgenii
#65M06 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1712.05185

Abstract

The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schrödinger-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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