Hi,

Can anybody show me how to derive the 2N optimized RUNGE KUTTA scheme from the ordinary fourth stage fourth order RK scheme.I want to understand the method.

Thank You Vasanth

hi Vasanth,

http://acoustique.ec-lyon.fr/publi/aiaa_2004_2814.pdf check this site for the optiomized code, you can also check the references section at the end of paper where you acn find the the references number listed behind 2,12, 13,14. You can refer these references to find your answer.

TC

Vasanth,

It's impossible to do it with either a Williamson or van der Houwen approach. You have to increase the number of stages to at least 5. One must be very specific about what "optimizing" the method implies. There are many, many optimization themes like leading order error, linear stability, nonlinear contractivity, internal stability, phase-error, boundary order reduction, storage, error control observability and controllability, etcetera.

http://scholar.google.com/scholar?q=williamson+runge+kutta&ie=UTF-8&oe=UTF-8&hl=en

If you want to understand Williamsons approach, look at his paper and recast the terms in conventional RK nomenclature so that you can assign groups of terms to the proper Butcher coefficient. For van der Houwen, it's just a matter of setting the lower left entries in the Burtcher array to the proper b_{i}.

Hi Runge_Kutta

Thank you very much for your link.It is helpful.I will go through it and let you know if I have any questions.

Thanks