一阶常微分方程非线性初值问题解的标准后向微分格式

Odekunle
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摘要

本文描述了一阶常微分方程非线性初值问题数值解的一种新的非线性后向微分格式。该格式基于正则多项式的有理插值。它们是a稳定的。实验结果表明,该方法比欧拉反推法和奇异点附近梯形法具有更好的求解效果。关键词:逆向微分方案,配置,初值问题。数学学报Vol.3(1) 2004: 57-63
本文章由计算机程序翻译,如有差异,请以英文原文为准。
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR SOLUTION OF NONLINEAR INITIAL VALUE PROBLEMS OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give better results than Euler backward method and trapezoidal method near a singular point. KEY WORDS: backward differentiation scheme, collocation, initial value problems. Global Jnl Mathematical Sciences Vol.3(1) 2004: 57-63
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