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

SSP Coefficients of optimal methods
• First Order

  The backward Euler method is unconditionally SSP. Within the class of general linear methods, only first order methods can be unconditionally SSP.

• Second Order

The implicit trapezoidal rule is optimal with coefficient c=2.

• Third Order