Abstract
In this paper we constructed an exponentially fitted difference scheme for singular perturbation problem of hyperbolic-parabolic partial differential equation. Not only do we take a fitting factor in the equation, but also we put one in the approximation of second initial condition. By means of the asymptotic solution of singular perturbation problem we proved the uniform convergence of this scheme with respect to the small parameter.
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Vishik, M. I. and L. A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with a small parameter,AMS Translations,20, 2 (1961), 239–364.
Su Yu-cheng,The Methods of Boundary Layer Corrections in Singular Perturbations Scientific Technique Press, Shanghai (1983). (in Chinese)
Il'in, A. M., Differencing scheme for a differential equation with a small parameter affecting the highest derivative,Math. Notes,6, 2 (1969), 596–602.
Zlamal, M., On the mixed boundary value problem for a hyperbolic equation with a small parameter,Czech. Math. J.,84, 9 (1959), 218–242. (in Russian)
Doolan, E. P., J. J. H. Meller and W. H. A. Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin (1980).
Su Yu-cheng and Wu Chi-kuang,Numerical Method for Patial Differential Equations, Science Press, Beijing (1979). (in Chinese)
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Communicated by Su Yu-cheng
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Jin-reng, S. A difference method for singular perturbation problem of hyperbolic-parabolic partial differential equation. Appl Math Mech 7, 161–169 (1986). https://doi.org/10.1007/BF01897059
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DOI: https://doi.org/10.1007/BF01897059