Prerequisites: 16:198:510. Classes of computer methods: methods of points, methods of lines, finite elements, Ritz-Galerkin-type methods. Examples of simple computer programs. Stability, Consistency and Convergence. Hyperbolic equations. Basic properties, methods of solution, including the method of characteristics. Computer implementation, the relations between boundary conditions and extraneous solutions. Parabolic equations. Difference methods. Numerical stability ADIP method. Galerkin and finite element methods. Elliptic equations. Introduction to finite difference methods - detailed analysis of the finite element method.