In this article, a pseudospectral approach based on radial basis functions is considered for the solution of the standard Fitzhugh-Nagumo equation. The proposed radial basis function pseudospectral approach is truly mesh free. The standard Fitzhugh-Nagumo equation is approximated into ordinary differential equations with the help of radial kernels. An ODE solver is applied to solve the resultant ODEs. Shape parameter which decides the shape of the radial basis function plays a significant role in the solution. A cross-validation technique which is the extension of the statistical approach leaveone-out-cross-validation is used to find the shape parameter value. The presented method is demonstrated with the help of numerical results which shows a good understanding with the exact solution. The stability of the proposed method is demonstrated with the help of the eigenvalues method numerically. KeywordsFN equation, Radial basis function, Meshless.

中文翻译：

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求解标准Fitzhugh-Nagumo方程的径向基函数伪谱方法

在本文中，考虑使用基于径向基函数的伪光谱方法来求解标准Fitzhugh-Nagumo方程。所提出的径向基函数伪谱方法是真正无网格的。在径向核的帮助下，标准的Fitzhugh-Nagumo方程近似为常微分方程。ODE求解器用于求解所得的ODE。决定径向基函数形状的形状参数在解决方案中起着重要作用。交叉验证技术是统计方法“无人交叉验证”的扩展，用于查找形状参数值。数值结果帮助演示了所提出的方法，该方法对精确的解决方案有很好的理解。借助特征值方法，数值证明了所提方法的稳定性。关键词FN方程，径向基函数，无网格。