ABSTRACT
The Homotopy Levenberg-Marquardt Algorithm is used to solve singular non-linear equations that are constructed by the plasma equilibrium composition model according to mass action law and settle a matter that is sensitive to the initial iteration values. The homotopy equation, H ( x ,t) = tF ( x )+(1-t) G ( x ), is established by introducing auxiliary equation G ( x ) and homotopy factor sequence [t k]. The auxiliary equation is plasma equilibrium composition at high temperature and assumes that it contains only electron and the highest atomic cation of atoms, such as T max = 30000 K. The homotopy factor sequence [t k] is arranged in geometric, and the change of difference value of t k − t k-1 from large to small guarantees the continuity of the whole process. Finally, the Mg-CO mixture plasma for melting magnesium oxide crystals is taken as an example to verify the feasibility, the solution accuracy is less than 1 × 10-15, and the particle distribution at atmospheric pressure from 300 to 30,000 K was calculated.
