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A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation. (English) Zbl 1427.65285

Summary: In this paper, we propose a method to solve the Kadomtsev-Petviashvili equation based on splitting the linear part of the equation from the nonlinear part. The linear part is treated using FFTs, while the nonlinear part is approximated using a semi-Lagrangian discontinuous Galerkin approach of arbitrary order.
We demonstrate the efficiency and accuracy of the numerical method by providing a range of numerical simulations. In particular, we find that our approach can outperform the numerical methods considered in the literature by up to a factor of five. Although we focus on the Kadomtsev-Petviashvili equation in this paper, the proposed numerical scheme can be extended to a range of related models as well.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)

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