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守恒型奇摄动常微分方程混合边值问题的数值解法 被引量:4

Numerical Solution to Conservative Form and Singular Perturbed Ordinary Differential Equation with Mixed Boundary Condition
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摘要 本文考虑守恒型奇摄动常微分方程混合边值问题的数值解法,构造一个非守恒型差分格式,证明该格式一阶一致收敛.对第一边值问题,改进了文[1]的结果. A numerical solution is presented by the authorsto the conservative form and singular perturded ordinary differential equation with mixed boundary condition.To this end,a non-conservative form differeuce scheme is con- structed The scheme is proved to be uniformly converged to the so- lution of differential equation in order one.For the first boundary value problem, the result of literature hes got its improvement.
作者 蔡新 林鹏程
机构地区 华侨大学 福州大学
出处 《华侨大学学报(自然科学版)》 CAS 1990年第4期344-352,共9页 Journal of Huaqiao University(Natural Science)
关键词 守恒方程 常微分方程 奇摄动 混合边界 一致收敛 conservation equations ordinary differential equatiens singular perturbation compound boundary uniform convergence
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同被引文献10

  • 1林鹏程 江本锆.奇异摄动的周期边界问题[J].应用数学和力学,1987,8(10):877-883.
  • 2Kellogg R B, Tsan A. Analysis of some difference approximations for a singular perturbation problem without turning points[J] Math Comp, 1978, 32: 1025-1039.
  • 3Miller J J H, O'Riordan E, Shishkin G I. Fitted Numerical Methods for Singular Perturbation Problems [ M ]. Singapore:World Scientific, 1996.
  • 4Cai X, Liu F. Uniform Convergence Difference Schemes for Singularly Perturbed Mixed Boundary Problems [ J ]. J Comp Math, 2004, 166:31-54.
  • 5Farrell O, Hegarty A F, Miller J J H, et al. Parameter Robust Computational Methods for Singular Perturbed Differential Equations [M]. New York: CRC Press, 2000.
  • 6Liu F, Bhatia S K, Barzhi I I A. Numerical solution of hyperbolic models of trangsport in bidisperse solids [ J ]. Comp.Chen Enq, 2000, 24:1981-1995.
  • 7Liu F, Mcelwain. Solution of moving-boundary problems in finite media [J]. Journal of Applied Mathematics, 1997,59:71-84.
  • 8Doolan E P, Miller J J H, Schilders WHA. Uniform Numerical Methods for Problems with Initial and Boundary Layers[M]. Dublin: Boole Press, 1980.
  • 9R B Kellogg,A Tsam.Analysis of some Difference Approximations for A Singular Perturbation Problem Without Tuming Points[J].Math Comp,1978,32:1025-1039.
  • 10林鹏程.小参数常微分方程守恒型差分格式的一致收敛性[J].应用数学和力学,1986,7(11):993-1001.

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