Numerical Renormalization Group Calculations For Similarity Solutions and Travelling Waves

Details Numerical Renormalization Group Calculations For Similarity Solutions and Travelling Waves Numerical Renormalization Group Calculations For Similarity Solutions and Travelling Waves

1994-12-09

arxiv.org/abs/chao-dyn/9412005v1

Physics

Condensed Matter

14 pages, Postscript file of paper and 3 figures distributed as self-unpacking uuencoded compressed tar file.Also available by

Scientific paper

10.1103/PhysRevE.51.5577

We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and travelling waves. We show that for a large class of well-localized initial conditions, successive iterations of an appropriately defined discrete RG transformation in space and time will drive the system towards a fixed point. This corresponds to a scale-invariant solution, such as a similarity or travelling-wave solution, which governs the long-time asymptotic behavior. We demonstrate that the numerical RG method is computationally very efficient.

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