Approximation of equation of state presented by table to calculate gas-dynamics problems

To utilize EQS given by table in gas-dynamics calculus their analytical presentation is useful. One considers a case when pressure and inner energy depend on temperature and density. The simplest bilinear approximation of table cell does not satisfy to thermodynamic identity. The algorithms without this principal defect are elaborated. The approximated functions are constructed as linear combinations by 8 particular solutions satisfying to thermodynamic identity. Formulas of solution of 8-order system of linear equations for coefficients are obtained. It arises from coincidence of two predicted function values in four corners of table cell.