Solving nonstiff higher order ODEs directly by the direct integration method

Abstract

The variable order and stepsize direct integration (DI) method for solving systems of nonstiff higher order ODEs directly is reviewed. Mention is also made of the current inroads in solving stiff higher order ODEs directly. The advantages of the DI method over the corresponding Adams method when used to solve the same problem as a first order system are pointed out. Numerical results are presented comparing the two methods in terms of execution times for each tolerance used and execution times for each solution of the same range of accuracy.