Abstract:
This study presents a computational approach using a piecewise mesh to solve singularly
perturbed reaction-diffusion problems. The stability of the formulated scheme is thoroughly
analyzed. Several numerical examples are provided to demonstrate the method’s effectiveness.
The results confirm that the method achieves high accuracy and efficiency, with reduced
maximum absolute errors and improved convergence order. Additionally, the proposed
approach outperforms several existing methods in terms of solution precision. Numerical
experiments show enhanced convergence with fewer errors, supporting the theoretical analysis.
As a result, the method proves to be highly effective in approximating exact solutions.
