摘要
利用指数矩阵的精细算法及精度较高的柯特斯积分方法,并将二者结合,形成柯特斯精细积分法。文中推导了该方法的计算过程,讨论了该方法的稳定性。该方法运用柯特斯积分方法求解精细积分法中的向量积分,不仅避免了矩阵求逆和实际工程中逆矩阵不存在的问题,方便算法的编程,保证了算法在大型实际结构工程中的应用,而且无需对非齐次项进行数学拟合。该方法的精度取决于柯特斯积分的精度。算例结果表明,柯特斯精细积分法具有较高的可靠性,能较好地适应结构的动力反应分析。
Precise Cotes integration method was proposed by combining precise exponential matrix calculation and higher accurate Cotes integration. Calculation process and stability of this new method were developed and discussed. The new method uses Cotes formula to solve vector integration. It avoids the difficulty of the inverse matrix calculation, makes it convenient to program and ensures to apply this method in actual structure engineering. In particular, it is unnecessary to approximate the non-homogeneous vector in this new scheme. The accuracy of the method mainly depends on that of Cotes integration. Numerical examples are given to demonstrate the validity and efficiency of the algorithm.
出处
《四川建筑科学研究》
北大核心
2008年第2期11-13,共3页
Sichuan Building Science
基金
国家自然科学基金资助项目(10572107)
关键词
精细指数运算
柯特斯积分
稳定性
precise exponential matrix calculation
Cotes integration
stability
