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)
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.
The standard approach to applying IRK methods in the solution of two-point boundary value problems involves the solution of a non-linear system ofn×s equations in order to calculate the stages of the method, wheren is the number of differential equations ands is the number of stages of the implicit Runge-Kutta method. For two-point boundary value problems,(More)
Parameter Estimation for ODEs and DDEs is an important topic in numerical analysis. In this talk, we present a novel approach to address this inverse problem. Cross-entropy algorithms are general algorithm which can be applied to solve global optimization problems. The main steps of cross-entropy methods are first to generate a set of trial samples from a(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 step-size or order. This updating technique is shown to be applicable to a wide(More)