Uniform Difference Scheme for a Singularly Perturbed Linear 2nd Order Hyperbolic Problem with Zeroth Order Reduced Equation

Su Yu-cheng; Lin Ping

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Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(4): 283-294

Su Yu-cheng, Lin Ping. Uniform Difference Scheme for a Singularly Perturbed Linear 2nd Order Hyperbolic Problem with Zeroth Order Reduced Equation[J]. Applied Mathematics and Mechanics, 1990, 11(4): 283-294.

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Uniform Difference Scheme for a Singularly Perturbed Linear 2nd Order Hyperbolic Problem with Zeroth Order Reduced Equation

Nanjing University, Nanjing

Received Date: 1989-02-02
Publish Date: 1990-04-15

Abstract

Abstract

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.

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References(4)

References

[1]	Butuzov,V.F.,Corner boundary layer in mixed singularly perturbed problem for hyperbolic equations,Matematiceskii Sbornik,104,3(1977).
[2]	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,June(1988).
[3]	Lees,M.,Energy inequalities for the solution of differential equations,Trans.Amer.Math.Soc.,94,1(1960),58-73.
[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).