连续法研究进展及其应用

Evolution and Application of Continuation Method

非线性问题在许多应用学科中存在,由于其难以求解而限制了诸学科的发展,因此寻求一种有效的非线性方程求解方法具有重要意义。介绍了在复数域内求多项式方程组全部解的连续法和在实数域内求任意非线性方程组多组实数解的实数连续法,讨论了两种方法的应用情况,通过实例比较了两种方法的计算效率,为工程中非线性问题的求解提供了有效的途径。

TThere are nonlinear problems in many applied fields. Usually they are very difficult to solve. So it is especially necessary for us to introduce an effective method for solving nonlinear equations. The general continuation method which can find all solutions to polynomial equations in complex field and the real continuation method which can find part of real solutions to polynomial equations in real field are introduced. Their applications are discussed and their efficiency are evaluated through examples. This paper provides an effective way to solve non-linear problems in engineering.