四阶常微分方程奇异摄动问题的二阶精度差分解法

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Second-Order Accurate Difference Method for the Singularly Perturbed Problem of Fourth-Order Ordinary Differential Equations

摘要: 本文对一类四阶常微分方程边值问题建立了二阶一致精度的差分格式.本格式对步长h具有O(h²)阶的精度,大大改进了[1]的结果.

Abstract: In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.

[1]	孙其仁,一类四阶拟线性常微分方程奇异摄动问题的一致收敛差分解法,《MMMI会议文集》,上海(1987)
[2]	Il'in,A.M.Differencing scheme for a differential equation with a small parameter affecting the highest derivative,Math.Notes Acad.Sci.USSR.,6(1969),569-602.
[3]	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).
[4]	Stynes,M.and E.O'Riordan,A uniform accurate finite element method for a singular perturbation problem in conservative form,SIAM J.Numer.Anal.,23,2,(1986),369-375.
[5]	O'Riordan,E.and M.Stynes,An analysis of a superconvergence result for a singularly perturbed boundary value problem,Math.Comp.,46,173(1986),81-92.