3 papers
math.NA2023
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…
math.NA2023
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.…
math.NA2023
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…