Optimal Methods

• For nonlinear/nonautonomous systems:
  • Explicit methods
    • Runge-Kutta
    • Multistep
  • Implicit methods
    • Runge-Kutta
    • Multistep

• For linear, autonomous systems:
  • Explicit methods
    • Runge-Kutta
    • Multistep
  • Implicit methods
    • Runge-Kutta
    • Multistep

Matlab Scripts

Maple Scripts

• First Order

  Optimal first order explicit SSP Runge-Kutta methods consist simply of repeated forward Euler steps. These methods all have effective SSP coefficient equal to unity and are equivalent to simply using the forward Euler method.

• Second Order
• Third Order
• Fourth Order
• Higher Order

  Explicit SSP Runge-Kutta methods have order at most equal to four.