A MULTIRESOLUTION METHOD FOR NUMERICAL REDUCTION AND HOMOGENIZATION OF NONLINEAR ODES

The multiresolution analysis (MRA) strategy for the reduction of a non linear differential equation is a procedure for constructing an equati on directly for the coarse scale component of the solution. The MRA ho mogenization process is a method for building a simpler equation whose solution has the same coarse behavior as the solution to a more compl ex equation. We present two multiresolution reduction methods for nonl inear differential equations: a numerical procedure and an analytic me thod. We also discuss one possible appproach to the homogenization met hod, (C) 1998 Academic Press.