2 citations · 2 across the 11 of their papers we have counts for
11 papers
Error propagation in an explicit and an implicit numerical method for Volterra integro-differential equations
J. S. C. Prentice
We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global er…
Estimating the error term in the Trapezium Rule using a Runge-Kutta method
J. S. C. Prentice
We show how the error term for the Trapezium Rule can be estimated, by solving an initial value problem using a Runge-Kutta method. The error term can then be added to the Trapeziu…
An Euler-type method for Volterra integro-differential equations
J. S. C. Prentice
We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite T…
Stepwise global error control in Euler's method using the DP853 triple and the Taylor remainder term
J. S. C. Prentice
We report on a novel algorithm for controlling global error in a step-by-step (stepwise) sense, in the numerical solution of a scalar, autonomous, nonstiff or weakly stiff problem.…
Determining the Rolle function in Hermite interpolatory approximation by solving an appropriate differential equation
J. S. C. Prentice
We determine the pointwise error in Hermite interpolation by numerically solving an appropriate differential equation, derived from the error term itself. We use this knowledge to…
Efficiency of the Multisection Method
J. S. C. Prentice
We study the efficiency of the multisection method for univariate nonlinear equations, relative to that for the well-known bisection method. We show that there is a minimal effort…
Enhancing the accuracy of the Taylor polynomial by determining the remainder term
J. S. C. Prentice
We determine the Lagrange function in Taylor polynomial approximation by solving an appropriate initial-value problem. Hence, we determine the remainder term which we then approxim…
Determining the Rolle function in Lagrange interpolatory approximation
J. S. C. Prentice
We determine the Rolle function in Lagrange polynomial approximation using a suitable differential equation. We then propose a device for improving the Lagrange approximation by ex…
Global Error Control in the Runge-Kutta Solution of a Hamiltonian System using the RKQ Algorithm
J. S. C. Prentice
We study the effect of global error control in the numerical solution of Hamiltonian systems. In particular, we apply the RKQ algorithm in the numerical solution of a Hamiltonian s…
Nystrom Methods in the RKQ Algorithm for Initial-value Problems
J. S. C. Prentice
We incorporate explicit Nystrom methods into the RKQ algorithm for stepwise global error control in numerical solutions of initial-value problems. The initial-value problem is tran…
Runge-Kutta Methods: Local error control does not imply global error control
J. S. C. Prentice
We study the relationship between local and global error in Runge-Kutta methods for initial-value problems in ordinary differential equations. We show that local error control by m…