Abstract: A computational scheme of Runge-Kutta method is presented for Grüneisen state equation with adiabatic impact relation.Thermodynamic state variables,including pressure,Grüneisen coefficient,cold pressure,cold energy and pressure,as a function of specific volume are calculated.Numerical states parameters of tungsten at high-pressure are given.The curves of γ~V,E_K~V,P_K~V,P~V of tungsten are obtained and the P~V result agrees well with the experiment.Numerical solutions of f(P,T,V₁)=0 and f(P,T,V₂)=0 in two compressive states show that the effect of temperature on pressure is less than that of specific volume.

Key words: EOS with high-pressure, Runge-Kutta method, relation of P-V