Research on stepsize control in the BDF method for solving differential-algebraic equations

Research on stepsize control in the BDF method for solving differential-algebraic equations
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微分代数方程BDF法求解步长控制研究

DOI：
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发表时间：
1994
期刊：
International Symposium on Circuits and Systems
影响因子：
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通讯作者：
W. Mathis
W. Mathis
中科院分区：
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文献类型：
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作者：
M. Zhuang;W. Mathis

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针对刚性微分代数方程（DAE）问题的数值求解问题，提出了一种基于后向微分公式（BDF）方法的变设定值和预测步长比例积分微分（PID）控制。一般分析和数值试验表明，步长控制器大大改善了BDF算法的性能。建议的步长控制的实施是简单的。文中还包括两个非线性电路的数值试验结果。&lt;<ETX>&gt;
A proportional-integral-differential (PID) stepsize control with variable setpoint and prediction in the backward differentiation formulas (BDF) method is proposed for the numerical solution of stiff and differential-algebraic equation (DAE) problems. General analysis and numerical tests indicate that the stepsize controller improves the properties of the BDF algorithm considerably. The implementation of the proposed stepsize control is simple. The numerical test results of two nonlinear circuits are included.<<ETX>>