Scholarlink

<p>The work presented a numerical solution of the parabolic delay convection diffusion equations involving a singular perturbation, coupled with an integral boundary condition. Adopting a numerical scheme uniform with regard to the perturbation parameter, utilizing the implicit Euler scheme as a solution approach with respect to the time component, as well as a cubic spline with tension approach as a solution scheme with respect to space components, to which the simulation of an integral boundary condition is done by adopting the Simpsons 1/3 rule. It should be noted here that this numerical approach does not require any a priori information related to the value or position related to boundary layers. Uniform convergence and a related stability are presented as a second order related to space component alongside a first order related to time. The method’s applicability is demonstrated using numerical examples, reproducing the convergence order correctly as presented by this theory.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Stable and uniform numerical scheme for parabolic delay convection–diffusion equations involving singular perturbation and integral boundary conditions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月23日

查看全文
  • Wondimagegnehu Simon Hailu,
  • Gemechis File Duressa

摘要

The work presented a numerical solution of the parabolic delay convection diffusion equations involving a singular perturbation, coupled with an integral boundary condition. Adopting a numerical scheme uniform with regard to the perturbation parameter, utilizing the implicit Euler scheme as a solution approach with respect to the time component, as well as a cubic spline with tension approach as a solution scheme with respect to space components, to which the simulation of an integral boundary condition is done by adopting the Simpsons 1/3 rule. It should be noted here that this numerical approach does not require any a priori information related to the value or position related to boundary layers. Uniform convergence and a related stability are presented as a second order related to space component alongside a first order related to time. The method’s applicability is demonstrated using numerical examples, reproducing the convergence order correctly as presented by this theory.