Numerical Methods for Partial Differential Equations, 7.5 ECTS

Description

Literature

• Kreiss Matrix Theorem
• H.-O. Kreiss, On Difference Approximations of the Dissipative Type for Hyperbolic Differential Equations. Comm. Pure Appl. Math., 17:335-353, 1964.
• P. D. Lax and L. Nirenberg, On Stability of Difference Schemes; a Sharp Form of Gårding's Inequality. Comm. Pure Appl. Math., 19:473-492, 1966.
• R. Vaillancourt, A Simple Proof of Lax-Nirenberg Theorems. Comm. Pure Appl. Math., 23:151-163, 1970.
• G. Strang, Accurate Partial Difference Methods II. Non-Linear Problems. Num. Math., 6:37-46, 1964.
• Excerpt from R. J. LeVeque, Numerical Methods for Conservation Laws, 1992
• T. Hagstrom. New results on absorbing layers and radiation boundary conditions. In Topics in Computational Wave Propagation, pp. 1-42, Springer-Verlag, 2003.
• B. Engquist and A. Majda. Absorbing boundary conditions for numerical simulation of waves. Math. Comp. 31(139):629-651, 1977.

Contents

• Introduction
• Stability
• Von Neumann analysis
• Energy method
• Normal mode analysis
• Convergence and consistency
• Nonlinear problems
• Practical approximations in space and time
• Discretization of boundaries
• Summation by parts operators
• Absorbing boundary conditions
• Methods for wave propagation

Schedule

Examination

• Homework 1
• Homework 2
• Homework 3
• Homework 4
• Homework 5

Contact