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<p>This work presents a new higher-order parameter-uniform spline numerical method for the solution of a singularly perturbed reaction-diffusion boundary value problem. A cubic spline in&#xa0;compression method on a modified Shishkin mesh is used to discretize the given singularly perturbed boundary value problem. The parameter-uniform convergence analysis of the present numerical method is well-established. The numerical method is theoretically almost fourth-order convergent. According to the computational results presented in the tables, the current method gives a higher-order numerical rate of convergence. The theoretical results are supported by two numerical examples.</p>

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A higher-order spline numerical method for a singularly perturbed reaction-diffusion boundary value problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月15日

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  • Fasika Wondimu Gelu,
  • Ahmed A. Al Ghafli,
  • Hassan J. Al Salman

摘要

This work presents a new higher-order parameter-uniform spline numerical method for the solution of a singularly perturbed reaction-diffusion boundary value problem. A cubic spline in compression method on a modified Shishkin mesh is used to discretize the given singularly perturbed boundary value problem. The parameter-uniform convergence analysis of the present numerical method is well-established. The numerical method is theoretically almost fourth-order convergent. According to the computational results presented in the tables, the current method gives a higher-order numerical rate of convergence. The theoretical results are supported by two numerical examples.