We have solved numerically the nonlinear partial differential equation that links speed of sound and compression factor subjected to boundary conditions in the gaseous phase. This method has as similar accuracy as other numerical method based on an initial-values numerical integration in the low-density regime, but for higher densities, this new approach is more accurate and less sensitive to errors in both boundary conditions and speed-of-sound. The method was tested by comparing our numerical calculations against a reference equation of state in the fluid region of densities up to the critical density and temperatures between slightly above the critical temperature and four times the critical temperature. We also analysed and estimated uncertainties of derived thermodynamic properties from this method. Finally, the method was applied to argon and ethane experimental data. (C) 2004 Published by Elsevier Ltd.