Error propagation of general linear methods for ordinary differential equations

J.C. Butcher; Z. Jackiewicz; W.M. Wright

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Error propagation of general linear methods for ordinary differential equations

机译：常微分方程一般线性方法的误差传播

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We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p + 2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p + 1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods.

机译：我们讨论一般微分方程的线性方法的误差传播，直到阶数为p + 2为止，其中p是方法的阶数。然后将这些结果应用于p阶方法和相邻p + 1阶方法的局部离散误差估计。数值实验的结果证实了这些估计的可靠性。这项研究在基于常规线性方法的算法的稳健逐步调整和顺序更改策略设计中具有应用。

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来源
《Journal of complexity》 |2007年第6期|p.560-580|共21页
作者
J.C. Butcher; Z. Jackiewicz; W.M. Wright;
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作者单位

Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand;

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原文格式 PDF
正文语种 eng
中图分类数理科学和化学;
关键词
general linear methods; nordsieck representation; error propagation; local error estimation for methods of adjacent orders; adaptive stepsize selection; stability analysis;

机译：一般线性方法;诺西克表示;误差传播;相邻阶法的局部误差估计;自适应步长选择;稳定性分析;

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2. Olver's error bound methods applied to linear ordinary differential equations having a simple turning point [J] . T. M. Dunster Analysis and applications . 2014,第4期

机译：Olver的误差界方法应用于具有简单转折点的线性常微分方程
3. On The Error Analysis Of The New Formulation Of One Step Method Into Linear Multi Step Method For The Solution Of Ordinary Differential Equations [J] . Fadugba S. Emmanuel Okunlola J. Temitayo International Journal of Scientific & Technology Research . 2012,第9期

机译：一阶法到线性多步法常微分方程新解法的误差分析
4. Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations [C] . H. De la Cruz, R.J. Biscay, F. Carbonell, International Conference on Computational Science(ICCS 2006) pt.1; 20060528-31; Reading(GB) . 2006

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5. Theta methods for nonlinear ordinary differential equations and error analysis [D] . Walker, Matthew 2014

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6. Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error [O] . Hongqi Xue, Hongyu Miao, Hulin Wu -1

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7. Error propagation of general linear methods for ordinary differential equations [O] . J. C. Butcher A, Z. Jackiewicz B, W. M. Wright C 2016

机译：常微分方程一般线性方法的误差传播
8. Discretization Errors of Perturbation Numerical Methods for Initial Value Problems in Ordinary Differential Equations [R] . Adam, G. 1981

机译：常微分方程初值问题扰动数值方法的离散化误差

Error propagation of general linear methods for ordinary differential equations

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