Abstract
We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and traveling waves. We show that for a large class of well-localized initial conditions, successive iterations of an approximately 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 traveling-wave solution, which governs the long-time asymptotic behavior. We demonstrate that the numerical RG method is computationally very efficient.
Original language | English (US) |
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Pages (from-to) | 5577-5581 |
Number of pages | 5 |
Journal | Physical Review E |
Volume | 51 |
Issue number | 6 |
DOIs | |
State | Published - 1995 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics