Application of Variational Iteration Method to a General Riccati Equation
Application of Variational Iteration Method to a General Riccati Equation
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变分迭代法在一般Riccati方程中的应用
DOI：
10.12988/imf.2007.07248
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
I. Hashim
中科院分区：
文献类型：
--
作者：
B. Batiha;M. Noorani;I. Hashim
本文将变分迭代法（VIM）应用于一般Riccati微分方程的求解。所考虑的方程包括一个变系数方程和一个矩阵方程。在VIM中，修正泛函由一般拉格朗日乘子构造，该乘子可通过变分理论识别。VIM以快速收敛级数的形式给出了近似解。与精确解和四阶RungeKutta法的比较表明，VIM是求解非线性方程的一种有效方法。本文为经典力学本科高级课程的教学和对技术的理解提供了有益的练习。
In this paper, the variational iteration method (VIM) is applied to the solution of general Riccati differential equations. The equations under consideration includes one with variable coefficient and one in matrix form. In VIM, a correction functional is constructed by a general Lagrange multiplier which can be identified via a variational theory. The VIM yields an approximate solution in the form of a quickly convergent series. Comparisons with exact solution and the fourth-order RungeKutta method show that the VIM is a powerful method for the solution of nonlinear equations. The present paper may be a suitable and fruitful exercise for teaching and better understanding techniques in advanced undergraduate courses on classical mechanics.