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<p>Radial basis function (RBF) interpolatory methods avoid the mesh generation and do not require iterative computations, making them popular numerical techniques for solving partial differential equations (PDEs) in aerodynamics and fluid dynamics. This paper adapts the construction of RBF interpolation into a pseudo-spectral methodology for computing both linear and nonlinear dispersive PDEs. The key strategy involves extracting differential matrix forms from the interpolant expressions, enabling the computation of first-order, second-order, and even higher-order derivatives. The efficacy and accuracy of the proposed approach are demonstrated by solving specific PDEs such as the Allen-Cahn equation, the Degasperis-Procesi equation and the Camassa-Holm equation.</p>

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Rbf-based quasi-interpolating pseudo-spectral method for solving nonlinear dispersive PDEs

  • 期刊论文

  • 发表日期：

    2025年8月7日

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  • Yanxia Lyu,
  • Xianchi Li

摘要

Radial basis function (RBF) interpolatory methods avoid the mesh generation and do not require iterative computations, making them popular numerical techniques for solving partial differential equations (PDEs) in aerodynamics and fluid dynamics. This paper adapts the construction of RBF interpolation into a pseudo-spectral methodology for computing both linear and nonlinear dispersive PDEs. The key strategy involves extracting differential matrix forms from the interpolant expressions, enabling the computation of first-order, second-order, and even higher-order derivatives. The efficacy and accuracy of the proposed approach are demonstrated by solving specific PDEs such as the Allen-Cahn equation, the Degasperis-Procesi equation and the Camassa-Holm equation.