Abstract: This technical paper describes a high-fidelity numerical framework for modeling shallow water solitary wave behavior described by the Korteweg-de Vries (KdV) equation via a MATLAB implementation of the Radial Basis Function Pseudo-Spectral (RBF-PS) method employing Gaussian basis functions and the adaptive ode113 time integrator. A systematic grid-refinement study is conducted, which reveals numerical ill-conditioning when fixed RBF shape parameters are employed. This problem is successfully resolved via a grid-dependent shape parameter search (e.g., s = [1.11, 1.20, 1.25] for n = [100, 200, 300]), leading to spectral-like convergence behavior. The presented framework is ascertained rigorously with analytical soliton solutions, conservation of physical invariants (mass and momentum), as well as extensive convergence studies covering both spatial (grid convergence) and temporal (time-step refinement) tests. These confirm the high-order accuracy, numerical stability and robustness of the method. The results here validate the proposed RBF-PS method as an accurate, robust and physically consistent computational procedure for simulating nonlinear dispersive wave physics. Furthermore, it highlights that choosing the shape parameter adaptively improves the accuracy and stability of RBF-based numerical methods.

Keywords: Grid convergence analysis, Korteweg-de Vries equation, Meshless collocation methods, Radial basis function pseudo-spectral method, Shape parameter tuning, Solitary wave simulation

Pages: 76-86

WSEAS Transactions on