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math.NA2025
Weighted finite difference methods for the semiclassical nonlinear Schrödinger equation with multiphase oscillatory initial data
Yanyan Shi, Christian Lubich
This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. W…
math.NA2025
A filtered finite difference method for a highly oscillatory nonlinear Klein--Gordon equation
Yanyan Shi, Christian Lubich
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with highly oscillatory initial data in the form of a modulated plane wave. In this regime, the s…