A Mesh‐Free Local Radial Basis Function‐Finite Difference Method for Solving Reaction‐Diffusion‐Convection Model

ABSTRACT This study proposes a numerical technique for obtaining approximate solutions of the Burgers–Fisher (BF) equation, a nonlinear reaction‐convection‐diffusion model characterized by the complex interplay of convection ( ), diffusion ( ), and ( ) terms. The scheme is based on combination of Crank–Nicolson scheme and local radial basis function method. Following this, Crank–Nicolson scheme is used for temporal derivative while the local radial basis function‐collocation approach is applied for the approximation of spatial derivatives. This hybrid strategy effectively captures the nonlinear dynamics while maintaining computational efficiency. The analysis also includes an investigation into the stability and convergence of the BF model within the and spaces. The proposed strategy demonstrates computational efficiency and low implementation cost, with numerical experiments on benchmark problems confirming its accuracy, robustness, and ability to resolve steep‐gradient solutions effectively.