Similarity, Self-similarity, and Intermediate Asymptotics (Consultants
- G. I. Barenblatt
We present a numerical implementation of the renormalization group (RG) for partial diierential equations, constructing similarity solutions and travelling waves. We show that for a large class of well-localized initial conditions, successive iterations of an appropriately deened discrete RG transformation in space and time will drive the system towards a xed 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 eecient.