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.
 Citation: 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.

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

• Received Date: 1989-02-02
• Publish Date: 1990-04-15
• 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.
•  [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).

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沈阳化工大学材料科学与工程学院 沈阳 110142

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