An introduction to the principles and application of numerical analysis and computer programming for the solution of partial differential equations. Emphasis is placed on those aspects which are most relevant to applications.
Selected topics in the following sequence:
- Short review of the classification of partial differential equations and the properties of their solution.
- Short review of relevant topics in calculus and numerical analysis.
- 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.
Homework assignments, computer programs, selected readings. A mid-term and a final examination.