Wayne H. Enright

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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)
We have recently developed a generic approach for solving neutral delay differential equations based on the use of a continuous Runge–Kutta formula with defect control and investigated its convergence properties. In this paper, we describe a method, DDVERK, which implements this approach and justify the strategies and heuristics that have been adopted. In(More)
Numerical methods for partial differential equations often determine approximations that are more accurate at the set of discrete meshpoints than they are at the “off-mesh” points in the domain of interest. These methods are generally most effective if they are allowed to adjust the location of the mesh points to match the local behavior of the(More)
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 stepsize or order. This updating technique is shown to be applicable to a wide(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.
Most methods for solving stLff systems are based on implicit formulas and require the use of Newtonlike iterations. The cost of the matrLx operations in the iteration scheme of these methods can be quite high. A new iteration scheme is developed which exploits the structure of the system and also allows fast updating of the iteration matrix after a stepsize(More)