Studies in approximation methods—II: Initial value ordinary differential equations

Abstract

A comparison of Runge—Kutta and orthogonal collocation methods is made for the solution of initial value ordinary differential equations. The direct connection between implicit Runge—Kutta and orthogonal collocation methods is shown for a certain class of initial value problems; this class being of importance to chemical engineering systems. A number of new semi-implicit Runge—Kutta methods which have an imbedded truncation error estimate feature and are A-stable are presented. Using some test systems these new algorithms are shown to be the most computationally efficient for initial value problems.