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A meshless multi-symplectic local radial basis function collocation scheme for the “good” Boussinesq equation

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  • Zhang, Shengliang

Abstract

A novel meshless multi-symplectic scheme is proposed for the “good” Boussinesq equation. The scheme consists of a local radial basis function (RBF) collocation method (LRBFCS) in space and a symplectic integrator in time. The LRBFCS is simple and efficient, since only a sparse banded linear system has to be solved. Moreover, it can avoid the ill-conditioned problem and shape-parameter-sensitivity of the global RBF method. The multi-symplectic LRBFCS (MLRBFCS) is more accurate than traditional methods. Numerical experiments with uniform knots and random knots are designed to verify the effectiveness of the method.

Suggested Citation

  • Zhang, Shengliang, 2022. "A meshless multi-symplectic local radial basis function collocation scheme for the “good” Boussinesq equation," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s009630032200371x
    DOI: 10.1016/j.amc.2022.127297
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