Using a computational method for numerical homogenization, we perform the coarse-scale bifurcation analysis of nonlinear reaction-diffusion problems in both uniform and spatially varying media. The method is based on wavelet decomposition and projection of the differential equation on coarse scale wavelet spaces. The approach is capable of capturing turning points and pitchfork bifurcations of sharp, front-like solutions at the coarse level.
All Science Journal Classification (ASJC) codes
- Chemical Engineering(all)
- Computer Science Applications
- Bifurcation analysis
- Numerical homogenization
- Reaction-diffusion equations