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

Explicit linear multistep methods have the same SSP properties whether applied to linear or nonlinear equations.

SSP Coefficients of optimal methods
• First Order

  Optimal first order explicit SSP multistep 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 & Fourth Order