留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

具有初始跳跃的双曲型方程奇异摄动问题的数值解法

苏煜城 林平

苏煜城, 林平. 具有初始跳跃的双曲型方程奇异摄动问题的数值解法[J]. 应用数学和力学, 1990, 11(8): 665-670.
引用本文: 苏煜城, 林平. 具有初始跳跃的双曲型方程奇异摄动问题的数值解法[J]. 应用数学和力学, 1990, 11(8): 665-670.
Su Yu-cheng, Lin Ping. Numerical Solution of the Singularly Perturbed Problem for the Hyperbolic Equation with Initial Jump[J]. Applied Mathematics and Mechanics, 1990, 11(8): 665-670.
Citation: Su Yu-cheng, Lin Ping. Numerical Solution of the Singularly Perturbed Problem for the Hyperbolic Equation with Initial Jump[J]. Applied Mathematics and Mechanics, 1990, 11(8): 665-670.

具有初始跳跃的双曲型方程奇异摄动问题的数值解法

Numerical Solution of the Singularly Perturbed Problem for the Hyperbolic Equation with Initial Jump

  • 摘要: 本文考虑具有初始跳跃的二阶双曲型方程初边值问题.首先给出解的导数估计.然后在一非均匀网格上构造了一个差分格式,最后在能量范数意义下证明了差分格式解的一致收敛性.
  • [1] Vishik,M.I.and L.A.Lyusternik,On the asymptotic behavior of the solution of boundary value problems for quasilinear differential equations,Dokl.Akad.Nauk.,SSSR,121(1958).
    [2] Vishik,M.I.and L.A.Lyusternik,Initial jump for nonlinear differential equations containing a small parameter,Sov.Math.Dolk.,1(1960).
    [3] Kasymov,K.A.,On the asymptotic solution of the Cauchy problem with large initial conditions for nonlinear ordinary differential equations containing a small parameter,Usp.Math.Nauk.,17,5(1962).
    [4] Kasymov,K.A.,The initial jump problem for nonlinear system of differential equations containing a small parameter,Sov.Math.Dokl.,9(1968).
    [5] Kasymov,K.A.,Asymptotic solution of the Cauchy problem with initial jump for the second-order hyperbolic equation involving a small paramter,Sov.Math.Dokl.,195,1(1970).
    [6] Kasymov,K.A.and B.M.Kadykenov,On the Cauchy problem with initial jump for the singular perturbation linear hyperbolic equations degenerated to first order equation,Diff.Equations,19,12(1983).
    [7] Hsiao,G.C.and R.J.Weinacht,A singularly perturbed Cauchy problem,J.of Math.Anal.and Appl.,71(1979).
    [8] Hsiao,G.C.and R.J.Weinacht,Singular perturbations for a semilinear hyperbolic equation,SIAM J.Math.Anal.,14,6(1983).
    [9] Pěcenkina,A.A.,The solution of periodic problem for the second order ordinary differential equations with a small parameter multiplying the highest derivative,Diff.Equations with a Small Parameter,SSSR Akademy of Science,Ural'skii Scientific Centre,Sverdlovsk(1980).
    [10] Su Yu-cheng and Lin Ping,Numerical solution of singular perturbation problem forhyperbolic differential equation with characteristic boundaries,proceedings of the BAIL VConference,Shanghai,June(1988).
    [11] Doolan.E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problemswith Initial and Boundary Layers,Boole Press,Dublin(1980)
    [12] Lees,M.,Energy inequalities for the solution of differential equations,Trans.Amer.Math.Soc.,94,1(1960).
    [13] Shishkin,G.I.,Numerical solution of the boundary value problem for elliptic equations withsmall parameter at the leading derivative,USSR Computational Math.Math.Phys.,26,7-8(1986).
  • 加载中
计量
  • 文章访问数:  1571
  • HTML全文浏览量:  42
  • PDF下载量:  493
  • 被引次数: 0
出版历程
  • 收稿日期:  1989-06-04
  • 刊出日期:  1990-08-15

目录

    /

    返回文章
    返回