Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:222

Article

Nguyen-Ba, Truong¹  Sharp, Philip W.²  Vaillancourt, Remi¹ 

[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

[2] Univ Auckland, Dept Math, Auckland 1, New Zealand

关键词: General linear method for non-stiff ODE's;    Hermite-Birkhoff method;    Obrechkoff method;    Vandermonde-type systems;    Maximum global error;    Number of function evaluations;    CPU time;    DP(8,7)13M;    Comparing ODE solvers;   

DOI  :  10.1016/j.cam.2007.12.003

来源: Elsevier

【 摘 要 】

A four-stage Hermite-Birkhoff-Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form y' = f (t, y) with initial conditions y(t(0)) = y(0). Its formula uses y', y '' and y' as in Obrechkoff methods. Forcing a Taylor expansion of the numerical Solution to agree with all expansion of the true Solution leads to multistep- and Runge-Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the Values of Hermite-Birkhoff interpolation polynomials ill terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C++, HBOQ(14)4 is superior to the Domand-Prince Runge-Kutta pair DP(8,7)13M of order 8 ill solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is Superior to ode:113 in solving costly problems, oil the basis of the number of steps, CPU time, and maximum global error. The code is available oil the URL www.site.uottawa.ca/(-)rcmi. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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