A novel hybrid GFD-RBF method for convection-diffusion problems

Purpose This study aims to introduce a hybrid meshless method that combines generalized finite difference (GFD) with radial basis function (RBF) methods to solve nonlinear convection-diffusion problems, which frequently arise in heat transfer and fluid flow applications. Design/methodology/approach In the hybrid GFD-RBF method, lower-order derivatives (e.g. convection terms) are approximated using the GFD method, while higher-order derivatives (e.g. diffusion terms) are approximated using the RBF method. Findings The performance of the proposed hybrid method is evaluated on both linear and nonlinear problems, considering uniform and non-uniform node distributions within the domain. The results demonstrate the computational efficiency and effectiveness of the hybrid GFD-RBF method in solving second-order convection-diffusion problems. The developed method is also compared with finite difference and meshless methods. Originality/value This novel meshless method provides a new and efficient technique for solving nonlinear convection-diffusion problems.