Finite Difference Method on Piecewise Mesh for Singularly Perturbed Reaction Diffusion Equation with Robin Type Boundary Conditions

Abstract

In this study, we develop a finite difference approach on piecewise mesh to solve singularly perturbed reaction-diffusion equations with Robin boundary conditions. Two numerical examples are provided to demonstrate the method’s applicability. The results confirm that the maximum absolute error and convergence order validate the method’s accuracy. Moreover, the proposed approach outperforms several existing methods in terms of solution precision. Numerical experiments show improved convergence with fewer errors, reinforcing the theoretical analysis. Consequently, the method produces accurate solution in approximating exact solutions.