The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations on the Line.
Abstract
The long time behavior of the solutions of nonlinear parabolic initial value problems on the line has been investigated by many authors. In particular they have shown, under certain assumptions, the existence of traveling waves to which a large class of initial data eventually evolves. They have also proved that which traveling wave solution is picked out as the asymptotic state often depends on the behavior of the initial data at infinity. This causes difficulties for the numerical simulation of the long time evolution of such problems. In particular, if an aritificial boundary is introduced, the boundary condition imposed there must depend on the initial data in the discarded region. This work derives such boundary conditions, based on the Laplace transform solution of the linearized problems at + or - infinity. The authors illustrate their utility by presenting a numerical solution of Fisher's equation, a nonlinear parabolic equation with traveling wave solutions which has been proposed as a model in genetics. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1984
- Accession Number
- ADA139238
Entities
People
- H. B. Keller
- T. Hagstrom
Organizations
- University of Wisconsin–Madison