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Highly accurate method for solving initial boundary value problem for first order hyperbolic differential equations

Restrictive Taylor approximation is a new approach similar to Restrictive Pade' approximation mentioned in [2] is proposed. An explicit method for solving a first order wave equation is treated. The suggested method is of high accuracy whatever the exact solution is too large. It treats also the discontinuous behavior of the initial data for the function or its derivative. The stability condition and comparison between the considered method and Lax-Wendroff method are discussed.