An Efficient Algorithm for Solving Stiff Differential Equation System Adapted to Circuit Analysis

Tan Gen-lin; Liang Jian-xian

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An Efficient Algorithm for Solving Stiff Differential Equation System Adapted to Circuit Analysis

更新时间：2025-12-08

- An Efficient Algorithm for Solving Stiff Differential Equation System Adapted to Circuit Analysis
- Acta Electronica Sinica Issue 3, Pages: 84-91(1983)
- 作者机构：
  
  北京工业大学
- 作者简介：
- 基金信息：
- DOI：
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- Published：1983
- 稿件说明：
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[1]谈根林,梁建湘.适于电路分析的解刚性常微分方程的有效算法[J].电子学报,1983(03):84-91.

Tan Gen-lin, Liang Jian-xian. An Efficient Algorithm for Solving Stiff Differential Equation System Adapted to Circuit Analysis[J]. Acta Electronica Sinica, 1983, (3): 84-91.
[1]谈根林,梁建湘.适于电路分析的解刚性常微分方程的有效算法[J].电子学报,1983(03):84-91. DOI：

Tan Gen-lin, Liang Jian-xian. An Efficient Algorithm for Solving Stiff Differential Equation System Adapted to Circuit Analysis[J]. Acta Electronica Sinica, 1983, (3): 84-91. DOI：

摘要

本文基于不等距牛顿插值

简捷地导出了一个新的积分公式及其截断误差。新的算法比Gear、BDF、PBD方法稳定、有效

它的积分步数、牛顿迭代次数及Jacob修改次数均可明显减少。文中还讨论了自开始、自动变阶变步长、输出点插值以及程序组织方法

并用计算实例对算法的效果进行了检验。

Abstract

A new integration formula and its local truncation error are presented on the basis of non-iso-interval Newton interpolation. The new integration algorithm appears to be more stable and efficient than the methods of Gear

BDF

PBD. Its numbers of the integration steps

Newton iterations

Jacob modifications may be decreased significantly. The self-start

automatic variating order and step of the integration

the interpolation of output points and the structure of the integration program are discussed and the effect of the algorithm is assessed by using numerical caculations.

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