割线法计算二元相图

在分析相图计算原理及评述各种计算方法的基础上,提出了以扩展割线法(即单变量函数割线法的推广)计算Cu-Ni二元相图,在求解中采用前入数据,以扩展割线法进行迭代圆满地用计算机解出一组四元非线性方程组,与牛顿迭代法相比,此法无需求导、求逆及求雅可比矩阵等繁琐步骤,且对初值要求不苛,虽不像牛顿法以二阶收敛,但对方程数目不很多(其实三元系最多也只有8个方程)的相图计算,其收敛速度仍很可观,所需机时很短。

Extended Secant Method for the Phase Diagram Calculation of Binary Systems

Analyzing the principle of phase diagram calculation and reviewing various methods in earlier works, an extended secant method, ie.a generalization of the secant method for a single variable function, is developed to calculate the phase diagram of Cu-Ni binary system. Previous data by other authors are employed in the solution of such a phase diagram which is expressed as a quartery system of nonlinear equations, and a satisfactory computer-based solution is given by the iteration using the extended secant method. Comparing with the Newton's iteration, the present method need not such tedious steps as derivating, reversing and arranging the Jacobi matrix etc, moreover it requires not stringently the initial values assigned. A considerable convergence rate and hence the short operating time are provided if the number of equations is not too great (whereas for a ternary system there are eight equations at most) , though this method cannot converge like Newton's method by which the second order convergence is certain.