<p>We propose a numerical scheme to solve the third-order nonlinear Korteweg-de Vries (KdV) equation via the collocation-based radial basis function (RBF) method. In this work, we consider a hybrid radial kernel, i.e., the Gaussian-cubic kernel. This hybrid kernel is constructed by linearly combining smooth Gaussian radial functions with piecewise smooth cubic radial functions, which are then evaluated at the collocation points to approximate the numerical solution. The proposed scheme works similarly to the standard RBF with the collocation method. In the hybrid kernel, there is an additional parameter (weight parameter) over the shape parameter. We studied how these parameters influence the accuracy of the numerical results and how we determine them via particle swarm optimization (PSO). The proposed hybrid collocation method has been tested on various examples of KdV equations to evaluate its accuracy and efficiency compared with those of the traditional RBF method.</p>