在實際工程和科學計算中，經常會遇到求解高次代數方程或超越方程問題，我們把這些方程統(tǒng)稱為非線性方程。在非線性方程中，除了二次、三次、四次代數方程外，求解其他的方程不但沒有一般的公式，而且若只依據方程本身來判別是否有根及根的個數是很困難的。因此，我們需要尋求非線性方程根的比較精確的近似解。但是如果我們直接用在大學數學中學習的幾種傳統(tǒng)的方法求解不僅難度較大而且需要做大量繁雜的計算，本課題旨在利用MATLAB數學軟件,通過傳統(tǒng)的方程求解思路，編寫出對應的MATLAB程序來求解。這里主要有二分法、簡單迭代法、牛頓迭代法三種解題思路，編寫出程序后，再將這三種方法進行比較，判斷其優(yōu)劣。研究結果表明利用MATLAB數學軟件可以省略大量繁雜的計算，并使求解的精確度大大提高，且三種方法中牛頓迭代法收斂最快。
關鍵詞： MATLAB 非線性方程 二分法 簡單迭代法 牛頓迭代法 程序
Abstract
In practical engineering and scientific calculations, you often encounter the problem of the solution of higher order algebraic equations or transcendental equations, we put these equations are collectively referred to as non-linear equations. In non-linear equations, in addition to the quadratic, cubic and quartic equations, solving other equations not general formula, but if the only basis for the equation itself to identify whether there is a root and the number of roots are very difficult. Therefore, we need to find the roots of nonlinear equations more accurate approximate solution. But if we direct use the traditional method learned in College mathematics for solving not only difficult but also need to do a lot of complicated calculation, This topic is designed to use MATLAB mathematics software, through the traditional thinking, writing for the corresponding MATLAB programs to solve. Here mainly have dichotomy, simple iterative method, Iterative method Newton three thoughts, write a program, then compared these three methods to determine their advantages and disadvantages. The results show that the use of MATLAB software can omit a lot of complicated mathematical calculations, and make greatly improve the accuracy of the solution, and Iterative method Newton is the fastest convergence in the three methods.
Key words: MATLAB Nonlinear equations Dichotomy Simple iterative method Iterative method Newton Program
