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Smoothing effects on the IMR and ITR

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    R. P. K. Chan & N. Razali

  2. Fundamental Engineering Unit, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Malaysia

    N. Razali

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  1. R. P. K. Chan
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  2. N. Razali
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Correspondence to N. Razali.

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Chan, R.P.K., Razali, N. Smoothing effects on the IMR and ITR. Numer Algor 65, 401–420 (2014). https://doi.org/10.1007/s11075-013-9779-7

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  • DOI: https://doi.org/10.1007/s11075-013-9779-7

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