Finite differences method for numerical solution of hoph equation

In this thesis in general the numerical solutions of the initial and initial-boundary value problems for the first order nonlinear hyperbolic type are investigated. For this aim, at first the exact solution of the differential problem is found and differentiable properties are studied. It is proved that, the exact solution have the points of discontinuities the locations of which unknown before, if the initial profile has both a negative and negative slops.Therefore the classical solution the interest us problem does not exist. In order to find the weak solution, the special auxiliary problem is introduced. The suggested auxiliary problem permits us to apply the familiar method for finding the numerical solution.In the second part the algorithms for obtaining of the numerical solution of nonlinear Hoph equation are developed.Later, the initial-boundary value for the Hoph equation is obtained.Finish the process of the motion of the two phase fluids in porous medium is investigated.