A hyperbolic scalar PDE

A difference method

Stability

Dissipative approximations

**LECTURE 2: Initial value problems for hyperbolic PDE**

Systems in one space dimension

Wellposedness

Systems in several space dimensions

**LECTURE 3: Initial-boundary value problems (IBVP) for PDE**

A model problem

Analysis of wellposedness

The energy method

**LECTURE 4: Difference methods for IBVP, (I)**

A semidiscrete model problem

The energy method for stability analysis

The Laplace transform technique

The Kreiss condition

**LECTURE 5: Difference methods for IBVP, (II)**

Error estimates

The method of lines

Fully discrete approximations

Examples