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解一类奇异摄动两点边界值问题的Booster方法 被引量：2

Booster method for singularly perturbed two-point boundary value problems.
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摘要 研究一类奇异摄动两点边界值问题,用Booster方法进行求解,使其收敛阶提高了O(εn+ 1 ) ,尤其在特殊加密网格上,使其收敛阶从O(N- 2 )提高到O(εn+ 1 N- 2 ) .其中ε为摄动小参数,n为渐近展开的阶数.最后给出了数值例子. A Booster method is presented for the singluarly perturbed two-point boundary value problems. It improves the convergence by a factor of ε+{n+1}. Moreover, the convergence order is improved to O(ε+{n+1}N+ -2 ) from {O(N+ -2 )}in the special meshes, where ε is the small parameter and n is the order of the asymptotic approximation. Numerical results are presented in support of this claim.
作者 金中秋 梁克维 江金生
机构地区 浙江大学数学系 新加坡国立大学数学系
出处 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2005年第3期268-272,共5页 Journal of Zhejiang University（Science Edition）
基金 国家自然科学基金资助项目 (10 2 71112 ) 浙江省自然科学基金资助项目 (2 0 40 19)
关键词 奇异摄动两点边界值问题 Booster方法 渐近展开 收敛性 singularly perturbed problem Booster method asymptotic approximations convergence
分类号 O241.81 [理学—计算数学]
  • 相关文献

参考文献7

  • 1ISRAELI M, UNGARISH M. Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations [J]. Numer Math, 1982,39(3) :309-324.
  • 2NATESAN S, RAMANUJAM N. A "Booster method" for singular perturbation problems arising in chemical reactor theory[J]. Applied Mathematics and Computation, 1999,100 (1) 27- 48.
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  • 7岑仲迪,高怀毅.奇异摄动罗宾问题在Bakhvalov-Shishkin网格上的一致收敛有限差分法[J].浙江大学学报（理学版）,2004,31(4):373-375. 被引量：5

二级参考文献9

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  • 8梁克维,李大明,江金生.中点迎风差分格式在Bakhvalov-Shishkin网格上的注记[J].浙江大学学报（理学版）,2002,29(1):20-24. 被引量：8
  • 9金中秋,梁克维,江金生.修正的Bakhvalov-Shishkin网格上奇异摄动问题的一致收敛性[J].浙江大学学报（理学版）,2003,30(3):263-267. 被引量：2

共引文献4

同被引文献7

  • 1钱芝蓁,耿秀芬,张伟江.奇异摄动方程的样条函数解法[J].上海交通大学学报,1995,29(3):82-87. 被引量：1
  • 2[1]O Riordan E,Styne M.A uniformly accurate finite-element method for a singularly peturbed one-dimensional reaction-diffusion porblem[J].Math of Comp,1986,47(176):555-570.
  • 3[2]Israeli M,Ungarish M.Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approsimations[J].by incorporation of asymptotic approximations[J].Numer Math,1982,39(3):309-324.
  • 4[3]Natesn S,Ramanujam N.A"Booster method"for singular perturbation problems arising in chemical reactor theory[J].Applied Mathematics and Computation,1999,100(1):27-48.
  • 5[4]Ungarish M.Combination of asymptotic and numerical methods for the investigation of rotating compressible flows in a cylinder for small Rossby and Ekman numbers[D].Technion,Israel Institute of Technology,Haifa:Technion,Israel Institute of Technology,1980.
  • 6[5]Israeli M,Ungarish M.Improvement of numerical schemes by incorporation of approximate solutions applied to rotating compressible flows[A].Proceedings of the seventh International Conference on Numerical Methods in Fluid Dynamics,Stanford[C].1980,Lecture notes in Physics 141(W.C.Reynodls,R.W.MacCormack,eds).
  • 7程华,蔡静,么焕民.求解一类二阶奇异边值问题[J].哈尔滨师范大学自然科学学报,2008,24(6):24-26. 被引量：3

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浙江大学学报（理学版）
2005年 第3期

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