Approximation solutions of the wave problems

In the time dependent situations, the partial differential equations the most closely associated with the wave propagation are of hyperbolic type. Their role in the study of non-linear wave propagation is becoming increasingly important; and the knowledge of the properties of their solution is of considerable value when applications to the physical situations are to be made. Non linearity in wave occur in the evolution of discontinuous solutions from initial data propagates along their characteristics. To obtain accuracy in numerical integrations, small intervals and difference formulas are convenient immediately after crossing the characteristic curve. This work is intended to discussed several numerical solutions, for the two dimensional non-linear wave equations. The methods will be used involve successive approximation, characteristics, and finite difference methods.