Chapter 18 · Partial Differential Equations
18.12
Numerical Methods for PDEs
Real problems rarely have formulas. Replace derivatives by differences on a grid and march forward in time, keeping the step small enough for the method to stay stable.
About 15 minutes
You'll learn to
- →Approximate second derivatives with central differences
- →Take steps of the explicit method for the heat equation
- →Apply the stability conditions for heat and wave schemes
- →Solve Laplace's equation by averaging neighbors