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)
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.
Over the last decade several general purpose numerical methods for ordinary diier-ential equations (ODEs) have been developed which generate a continuous piecewise polynomial approximation that is deened for all values of the independent variable in the range of interest. For such methods it is possible to introduce measures of the quality 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)
Research in explicit Runge-Kutta methods is producing continual improvements to the original algorithms , and the aim of this survey is to relate the current state-of-the-art. In drawing attention to recent advances, we hope to provide useful information for those who apply numerical methods. We describe recent work in the derivation of Runge-Kutta… (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)