拟牛顿法求解化工过程数学模型

使用不需求取偏导数的拟牛顿法，求解化工过程模拟中产生的非线性方程组形式的数学模型。当未知数各分量间绝对值相差较大时，提出了改善收敛性的几种方法，即：（1）加入阻尼因子，以减少迭代值的震荡、（2）将方程适当降价；（3）将差商的绝对步长改为相对步长；（4）新迭代值超来其物理意义范围时，强制其回至其初始值。计算结果表明，与牛顿－拉夫森法相比，拟牛顿法不需求偏导数，对初值要求低，较雅可比迭代法收敛速度快，可用于求解化工过程的非线性方程组。

Solving Mathematical Model from Chemical Process by Quasi Newton Method

The sets of nonlinear equations can be solved by Quasi Newton method, and the calculated results show that it is more rapidly convergent than Jacobi iterative method and does not need partial derivatives of the functions involved in the equations while Newton|Raphson method does. In order to improve iterative convergence, some measures were proposed such as introducing relaxation factor into iterative form, reducing the number of equations and replacing absolute step sizes h by relative step sizes .