Numerical solution of the non-linear parabolic type equations with degeneration

In this thesis, structure of the solution of the nonlinear parabolic equation with two-time degeneration is investigated. In addition, the motion of the two phase fluids in layered denoting the movement of microscopic and analytical solution of this equation features removed and examined special cases. In partical case the exact solution of the maintained problem is found.In the last section of this thesis the efficient numerical algorithms for finding of the solution in a class of discontinuous functions is suggested. The theorem of convergence of the numerical solution to exact weak solutions is proved.In order to demonstrate the efficients of the proposed algorithm some computer tests have been made in some special cases.