A method for the computation of nonsimple turning points corresponding to cusps (Q1196866)

The author considers a problem of the type \(F(u,\alpha,\lambda)\equiv u- G(Ku,\alpha,\lambda)=0\), \(u\in U\), \(\alpha,\lambda\in\mathbb{R}\) where \(U\) is a Hilbert space, \(K\) is a compact operator from \(U\) to \(V\), \(V\) is a Banach space. \(G: V\times \mathbb{R}\times bbfR\to U\) is sufficiently smooth, and \((u^*,\alpha^*,\lambda^*)\) is a double turning point with respect to \(\alpha\) of \(F(u,\alpha,\lambda)=0\). The author presents a projection- iterative method for computing the nonsimple turning points, corresponding to cusp points, of the nonlinear operator equation. Finally, numerical examples illustrate the features of the proposed algorithm.