Numerical Differential Equations

1.Basic integration schemes. Order/control of accuracy.

2. Ordinary Differential Equations.

  • a. Initial Value (Cauchy) Problem: Euler method (forward-backward, explicit-implicit, stability). Order of the method. Runge-Kutta. Adaptive methods.
  • b. Boundary Value Problem. Shooting. Quasi-linearization. Continuation. 

3. Partial Differential Equations. Extensions from ODE. Numerical stability.