We present a discussion and description of a collection of FORTRAN routines designed to aid in the assessment of initial value methods for ordinary differential equations. Although the overall design characteristics are similar to those of earlier testing packages [2,6] that were used for the comparison of methods [5,7], the details and objectives of the… (More)
A general procedure for the construction of interpolants for Runge-Kutta (RK) formulas is presented. As illustrations, this approach is used to develop interpolants for three explicit RK formulas, including those employed in the well-known subroutines RKF45 and DVERK. A typical result is that no extra function evaluations are required to obtain an… (More)
ODEXPERT is a prototype knowledge-based system which selects the appropriate numerical solvers for initial value ordinary differential equations. It is capable of deriving some knowledge about the input problem by performing automated tests to detect properties and structures in the problem which guide the selection process.
In the numerical solution of large stiff systems of ordinary differential equations, matrix operations associated with the solution of linear equations often dominate the solution time. A matrix factorization is suggested that will allow efficient updating after a change in step-size or order. This updating technique is shown to be applicable to a wide… (More)
The quest for reliable integration of <i>initial value problems</i> (IVPs) for <i>ordinary differential equations</i> (ODEs) is a long-standing problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods implemented using standard floating point, where the onus lies entirely with the user to ensure the stepsize chosen is… (More)
of A decision tree to assist in the process of selecting an appropriate algorithm for the numerical solution of initial value ordinary differential equations is described. This initial value tree contains a series of questions that are intended to identify specific features of a user's problem, relevant to the selection of suitable software. An appropriate… (More)
Variable-order, variable-step multistep methods based on Adams formulas have proved very effective in the numerical solution of nonstlff systems of ordinary differential equations. The user specifies an accuracy parameter and the method attempts to produce a solution consistent with this accuracy requirement. The relationship between the global error in the… (More)