相平衡问题牛顿型方法的吸引域和临界曲线
Basins of attraction and critical curves for Newton-type methods in a phase equilibrium problem
摘要：
许多工程问题都是由非线性方程组描述的，这些方程组可能具有多个解，这对求根算法来说是一个挑战。多个解的存在可能会导致算法中解的复杂吸引域，严重影响算法的收敛性。本文研究了平面上有两个解的相平衡问题，即二元混合物中双异方体的计算中，吸引域与临界曲线（方程组的雅可比矩阵的奇点轨迹）的关系。结果表明，结合使用的吸引盆和临界曲线可以是一个有用的工具，以选择最合适的算法为特定的问题。
英文摘要：
Many engineering problems are described by systems of nonlinear equations, which may exhibit multiple solutions, in a challenging situation for root-finding algorithms. The existence of several solutions may give rise to complex basins of attraction for the solutions in the algorithms, with severe influence in their convergence behavior. In this work, we explore the relationship of the basins of attractions with the critical curves (the locus of the singular points of the Jacobian of the system of equations) in a phase equilibrium problem in the plane with two solutions, namely the calculation of a double azeotrope in a binary mixture. The results indicate that the conjoint use of the basins of attraction and critical curves can be a useful tool to select the most suitable algorithm for a specific problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
