Two classes of explicit generalized runge-kutta processes for non- stiff systems of ordinary differential equations

Abstract

The computation of non-stiff systems of ordinary differential equations can be accomplished with explicit Runge-Kutta methods. A class of explicit Generalized Runge-Kutta is described which requires an accurate evaluation of a Jacobian at every step. Second and fourth order processes are also described. In addition a second class of explicit Generalized Runge-Kutta is introduced which requires that the Jacobian be evaluated less than once every step. Finally a third order process is described. It is shown that these methods lend themselves easily to the development of error estimators similar to those of Fehlberg or England.

Keywords:

• Ordinary differential equations
• non-stiff ordinary differential equations
• runge-kutta method
• generalized runge-kutta method