I work with Jameson method and I would like to find something about the coefficients of the Runge-Kutta time stepping scheme (three and five stages, specially). I am interested in rigorous mathematical analysis of this method, since I haven't seen much of it myself. Can anyone please help me?

See

C.-W. Shu and S. Osher, Ecient implementation of essentially non-oscillatory shock capturing schemes, Journal of Computational Physics, v77 (1988), pp.439-471.

Chi-Wang Shu, "Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws", ICASE Report No.97-65.

Good Luck

(1). Runge-Kutta method to solve ordinary differential equation can be found in most numerical method books, see Carnahan. Luther, and Wilkes," Applied Numerical Methods" for detailed derivation and Fortran samples.

By Runge-Kutta methods I mean those used by Jameson. I don't think the mathematical analysis of such schemes is the same as that of the classical schemes. If I'm wrong, please correct me.

I've got some bibliography about them in

Jameson, A. "Transonic Flow Calculations", MAE Report #1651, 1983.

The problem is I can't find any. If you could help me, that would be very good!

They are:

Van der Houwen, "Construction of Integration Formulas for Initial Value Problems". North Holland, 1977.

Sonneveld, P. and van Leer, B., "Towards the Solution of van der Houwen's Problems", to appear in Nieuw Archief voor Wiskunde.

Roe, P. L., and Pike, J., "Reconstructing Jameson's Finite Volume Scheme for the Euler Equations", RAE Report, 1983.

Thank you for your attention!