Numerical Verffication of Simple Bifurcation Points

Abstract. Nonlinear boundary value problems (NBVPs in abbreviation) with pa-rameters are called parametrized nonlinear boundary value problems. This paper studies numerical verification of simple bifurcation points of parametrized NBVPs defined on one-dimensional bounded intervals. Around simple bifurcation points the original prob-lem is extended so that the extented problem has an invertible Fr\’echet derivative. Then, the usual procedure of numerical verification of solutions can be applied to the extended problem. A numerical example is given. Key words. parametrized nonlinear boundary value problems, numerical verification of solutions, simple bifurcation points AMS(MOS) subject classifications. $65L10,65L99$ Abbreviated title. Numerical Verificatio