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This paper is concerned with the numerical treatment of the first-order hyperbolic partial differential equation by small parameter with the time derivative term. This problem is reduced to stiff system of ODE, in time. The resulting system is solved by the restrictive Pad& approximation. The stability condition and the en-or upper bound are introduced. The numerical results are given and the considered method gives better results compared with the classical advantages of the considered method compared with the classical Pade' approximation.

RESTRICTIVE PADE' APPROXIMATION FOR SOLVING SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEM FOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION