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具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

苏煜城 张由余

苏煜城, 张由余. 具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式[J]. 应用数学和力学, 1992, 13(4): 279-286.
引用本文: 苏煜城, 张由余. 具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式[J]. 应用数学和力学, 1992, 13(4): 279-286.
Su Yu-cheng, Zhang You-yu. Difference Scheme for an Initial-Boundary Value Problem for Linear Coefficient-Varied Parabolic Differential Equation with a Nonsmooth Boundary Layer Function[J]. Applied Mathematics and Mechanics, 1992, 13(4): 279-286.
Citation: Su Yu-cheng, Zhang You-yu. Difference Scheme for an Initial-Boundary Value Problem for Linear Coefficient-Varied Parabolic Differential Equation with a Nonsmooth Boundary Layer Function[J]. Applied Mathematics and Mechanics, 1992, 13(4): 279-286.

具有非光滑边界层函数的线性变系数抛物型方程初边值问题的差分格式

Difference Scheme for an Initial-Boundary Value Problem for Linear Coefficient-Varied Parabolic Differential Equation with a Nonsmooth Boundary Layer Function

  • 摘要: 本文利用非均匀网格和指数型拟合差分方法给出了具有非光滑边界层函数的线性抛物型方程关于小参数ε一致收敛的差分格式.文章还给出了误差估计和数值结果.
  • [1] Butuzov,V.F.and A.V.Nesterov,On the asymptotics of the solution of an equation of parabolic type with small parameters affecting the highest derivatives,J.Vycisl.Mathem.and Mathem.Phys.,22,4(1982),865-870.
    [2] Shishkin,G.I.,Numerical solution of the boundary value problem for elliptic equations with small parameter at the leading derivative,USSR Computational Math.Math.Phys.,26,7-8(1986),1019-1031.
    [3] Bakhvalov,N.S.,The optimization of methods of solving boundary value problems with a boundary layer,USSR Computational Math.Math.Phys.,9,4(1969),841-859.
    [4] Doolan,E.P.,J.J.H Miller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin(1980).
    [5] Richards,Verga.,Matrix Iterative Analysis,Prentice Hall,Englewood Cliffs,N.J.(1962).
    [6] Friedman,A.,Partial Differential Equations of Parabolic Type,Prentice-Hall,Inc.(1964).
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出版历程
  • 收稿日期:  1990-12-25
  • 刊出日期:  1992-04-15

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