On smoothing and order reduction effects for implicit Runge-Kutta formulae
Journal of Computational and Applied Mathematics - Special issue on numerical methods for ordinary differential equations
A-stability of implicit Runge-Kutta extrapolations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Active and passive symmetrization of Runge-Kutta Gauss methods
Applied Numerical Mathematics
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This paper is a study of the effects of smoothing on the implicit midpoint rule (IMR) and the implicit trapezoidal rule (ITR) with implications for extrapolation of the numerical solution of ordinary differential equations. We extend the study of the well-known smoothing formula of Gragg to a two-step smoothing formula and compare the effectiveness of their use with the IMR and ITR for nonstiff and strongly stiff cases. We present an analysis of the Prothero-Robinson problem and as well as experimental results on linear and nonlinear problems.