The numerical treatment of perturbed bifurcation problems in ordinary differential equations

A new numerical method is presented to analyze perturbations of bifurcations of the solutions of nonlinear boundary value problems. The perturbations may result from imperfections or other inhomogeneities in the corresponding scientific problem. The nonisolated solutions are calculated in dependence of the perturbation parameter. Therefore, it is possible to determine the singular solution as well as a solution branch through this nonisolated solution simultaneously. Standard procedures of numerical analysis are applicable.