EGN 5456 Homework 2 Fall 1999

Consider the following one way wave equation with wave growth

u_t + a u_x = u + 1

You are to analyze this equation, propose a numerical scheme for it, and verify the performance of that scheme. You are looking for a simple explicit scheme, that allows time steps of the order of the spatial mesh size and has favorable numerical properties.

Some issues you must consider and correctly analyze:

• Properly posedness
• CFL condition
• Consistency
• Stability
• Convergence
• Accuracy
• Physically realistic boundary conditions
• Numerical effort

Verify the analysis numerically. Follow the good coding practices.