首页    期刊浏览 2025年07月08日 星期二
登录注册

文章基本信息

  • 标题:Higher-Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Differential Difference Equations with Mixed Small Shifts
  • 本地全文:下载
  • 作者:Mesfin Mekuria Woldaregay ; Gemechis File Duressa
  • 期刊名称:International Journal of Differential Equations
  • 印刷版ISSN:1687-9643
  • 电子版ISSN:1687-9651
  • 出版年度:2020
  • 卷号:2020
  • 页码:1-15
  • DOI:10.1155/2020/6661592
  • 出版社:Hindawi Publishing Corporation
  • 摘要:This paper deals with numerical treatment of singularly perturbed differential difference equations involving mixed small shifts on the reaction terms. The highest-order derivative term in the equation is multiplied by a small perturbation parameter ε taking arbitrary values in the interval 0,1 . For small values of ε , the solution of the problem exhibits exponential boundary layer on the left or right side of the domain and the derivatives of the solution behave boundlessly large. The terms having the shifts are treated using Taylor’s series approximation. The resulting singularly perturbed boundary value problem is solved using exponentially fitted operator FDM. Uniform stability of the scheme is investigated and analysed using comparison principle and solution bound. The formulated scheme converges uniformly with linear order before Richardson extrapolation and quadratic order after Richardson extrapolation. The theoretical analysis of the scheme is validated using numerical test examples for different values of ε and mesh number N .
国家哲学社会科学文献中心版权所有