Applied Mathematics and Mechanics (English Edition) ›› 1992, Vol. 13 ›› Issue (10): 909-916.

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A UNIFORM HIGH-ORDER METHOD FOR A SINGULAR PERTURBATION PROBLEM IN CONSERVATIVE FORM

吴启光, 孙晓弟   

  1. Department of Mathematics, Nanjing University, Nanjing
  • 收稿日期:1991-09-09 出版日期:1992-10-18 发布日期:1992-10-18

A UNIFORM HIGH-ORDER METHOD FOR A SINGULAR PERTURBATION PROBLEM IN CONSERVATIVE FORM

Wu Qi-guang, Sun Xiao-di   

  1. Department of Mathematics, Nanjing University, Nanjing
  • Received:1991-09-09 Online:1992-10-18 Published:1992-10-18

摘要: A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.

关键词: uniform high-order method, singular perturbation problem, initial value problem

Abstract: A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.

Key words: uniform high-order method, singular perturbation problem, initial value problem

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