An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem

Su Yu-chcng; Lin Ping

Volume 12 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(3): 219-227

Su Yu-chcng, Lin Ping. An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1991, 12(3): 219-227.

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An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem

Nanjing Unirersity, Nanjing

Received Date: 1990-04-24
Publish Date: 1991-03-15

Abstract

Abstract

In this paper we discuss, an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem.
- hyperbolic equation,
- singular perturbation,
- exponential fitting,
- difference scheme,
- boundary value problem

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References(6)

References

[1]	Su Yu-cheng and Lin Ping,Numerical solution of singular perturbation problem for hyperbolic differential equation with characteristic boundaries,Proceedings of the BAIL V Conference,Shanghai,Boole Press,Dublin 20-24 June(1988).
[2]	苏煊城、林平.具有零阶退化方程的二阶双曲型方程奇异摄动问题的一致差分格式,应用学数和力学,11,4 (1990),283-294.
[3]	苏爆城,林平,共有初始跳跃的双曲型万程奇异摄动问题的数值解,应用数学和力学,11,8(1990).665-676
[4]	Geel,R.,Singular Perturbations of Hyperbolic Type,Mathematical Centre Tracts 98,Amsterdam(1978).
[5]	Bobisud,L.E.,The second initial-boundary value problem for a linear parabolic equation with a small parameter,Mich.Math.J.,15,4(1969),495-504.
[6]	Lees,M.,Energy inequalities for the solution of differential equations,Trans.Amer.Math.Soc.,94.1(1960).

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