Hybrid radial kernel-based meshless method for the computational analysis of a two-dimensional Brusselator system

This article presents a simple and reliable kernel-based meshless approximation scheme to analyze the behavior of a two-dimensional coupled reaction–diffusion system. Combining the infinite smooth Gaussian radial kernel with a finitely smooth cubic radial kernel, a hybrid Gaussian-cubic kernel function is formulated to discretize the spatial differential operator. The solution is then advanced in time via a high-order ODE solver. An error estimate in terms of power function is derived providing a basis for the convergence of the proposed method. Stability and convergence of the proposed scheme are then numerically verified on several benchmark two-dimensional Brusselator systems. The outcomes verify the proposed scheme’s reliability, accuracy, efficiency, and simplicity against the available methods in the literature. •A meshless method of lines based on hybrid Gaussian-cubic radial kernel is proposed.•A nonlinear two-dimensional reaction-diffusion system is analyzed.•Error estimates are derived as a basis for further refined estimates.•Eigenvalues analysis confirms the method’s stable behavior.•Obtained results verify accuracy and efficiency over the existing kernel methods.