Regularization of the Solution to Degenerate Systems of Algebraic Equations Exemplified by Identification of the Virial Equation of State of a Real Gas

Thermodynamic calculation of a cycle in a two-phase region requires an equation of state of the working medium, which is used as a virial equation with unknown temperature functions. A degenerate system of algebraic equations has been constructed for unknown coefficients, which are the values of virial functions on a temperature mesh. Based on the regularization method, a variational-iterative algorithm for solving a degenerate system of equations has been developed. A computational experiment to confirm the effectiveness of the method was carried out.