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,… (More)

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… (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… (More)

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… (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… (More)

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… (More)

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… (More)

A popular approach for the numerical solution of boundary value ODE problems involves the use of collocation methods. Such methods can be naturally implemented so as to provide a continuous… (More)