摘要
研究了机械工程中常见两类非线性方程组全部解的获取问题.对于非线性多项式方程组,给出了应用同伦法无需选取初值求其全部复数解或实数解的数值算法.对于三角函数超越方程组,基于牛顿迭代法提出了一个数值方法,无需选取初值就可求出三角函数超越方程组在指定搜索区间的全部实数解.最后给出了数值实例证明了这些方法的正确性.
This paper discusses how to find the global set of solutions to two types of systems of nonlinear equations frequently encountered in mechanical engineering. One type is the system of nonlinear polynomial equations, and a numerical approach using the homotopy method is presented to work out all the complex or real solutions to the polynomial systems without initial value selection. The other type is the system of transcendental equations with trigonometric functions, and a numerical method based on Newton's iterative method is proposed, which can find all the real roots of the system of transcendental equations with trigonometric functions without initial value selection in the specified intervals. Numerical examples are given to confirm the validity of the numerical methods. The presented methods are ultraconvenient because there is no initial value selection in the root-finding procedure and can easily be implemented with computers.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2005年第1期71-74,102,共5页
Journal of Xidian University
基金
陕西省自然科学研究资助项目(2003E34)
西安电子科技大学青年科研工作站基金资助(020402)
