Adaptive continuation algorithms with application to combustion problems
The authors consider a path following algorithm to solve \(F(x,\lambda)=0\), F: \(R^ n\times {\mathbb{R}}\to {\mathbb{R}}^ n\) arising from discretization of a two point boundary value problem for an ordinary differential equation. Focusing on paths with simple turning points without bifurcation, the authors add a trivial equation \(\lambda '=0\) in order to keep the sparse structure of the Jacobian of F. They discuss various adaptive gridding techniques as well as the numerical implementation in great detail and present several numerical examples, for example methane-air flames (46 reactions). The paper is well organized and well written.
simple turning points without bifurcation
scientific article; zbMATH DE number 4111935
scientific article