In this thesis, a numerical method called Degenerate Matrix Method for solving nonlinear systems of differential equation, is studied. In this method unknown function and their derivative is approximated by means of Lagrange Interpolation .Matrix for derivative is always degenerate. By means of pseudo-invers of matrix for derivative the problem will be transformed to a problem of solving a system of onlinear equations. This system can be solved by an iteriative method. Application of DM method foe solving problems with PDEs is also considered. Illustrative examples are include to demonstrate the validity, accuracy and applicability of the DM method.