Optimized Methods

• For nonlinear nonautonomous systems:
  • Explicit methods
    • Runge-Kutta
    • Multistep
    • Multistep Multistage (MSRK)
  • Implicit methods
    • Runge-Kutta
    • Multistep

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

Matlab Scripts

Paper Scripts

Test Suite

Bibliography

Scripts for Runge-Kutta methods

• Manipulating the coefficient arrays:
  • butcher2shuosher.m - Generates Shu-Osher arrays for an explicit Runge-Kutta method, given the Butcher array.
  • shuosher2butcher.m - Generates Butcher array for a Runge-Kutta method, given the Shu-Osher arrays.
  • makebutcher.m - Generates Butcher arrays for various Runge-Kutta methods.
• Analyzing properties of the methods:
  • oc_butcher.m - Calculates order of accuracy of a Runge-Kutta method, given the Butcher array.
  • am_radius.m - Calculates radius of absolute monotonicity of a Runge-Kutta method, given the Butcher array.
  • rk_stabfun.m - Calculates stability function a Runge-Kutta method, given the Butcher array.