Numerical investigation of the second order nonlinear filtration equation in an absorbic media

In this thesis, the numerical solution of the first-kind initial-boundary value problem for the second order parabolic equation with a nonlinear source function in a class of discontinuous functions is investigated and the convergence of the numerical solution to the exact solution is proven. As known, the solution of various engineering problems can be reduced to the solutions of the Cauchy and initial-boundary value problems that solve degenerate parabolic class equations with nonlinear source functions. Since the solutions of these problems have some singularity, special investigation is required. The first chapter of the thesis establishes the required background. In the second chapter, the solution of the nonlinear heat equation in the form of a traveling wave in the half axis is obtained, and the differentiability of the solution is proven. Also, it is shown that the solutions are weak solutions. In the third chapter, the numerical solutions of the problems in the second chapter are investigated, and a-priori evaluations on the numerical solutions have been obtained.