Augmented Systems for the Computation of Singular Points in Banach Space Problems

We give a family of augmented systems as well as minimally extended systems which are suitable for the numerical detection and determination of singular points of Banach space problems. The systems are constructed in such a way that they only differ in a small part which must be adapted to the equivalence class to which the desired singular point belongs. The presented general results are specialized to the case of two-point boundary value problems.

[1]  Wolfgang Middelmann,et al.  Numerical Analysis of Perturbed Bifurcation Problems , 1998 .

[2]  Allan D. Jepson,et al.  The Numerical Solution of Nonlinear Equations Having Several Parameters I: Scalar Equations , 1985 .

[3]  M. Hermann,et al.  RWPM: a software package of shooting methods for nonlinear two-point boundary value problems , 1993 .

[4]  Robert D. Russell,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[5]  R. Seydel.  Numerical Computation of Primary Bifurcation Points in Ordinary Differential Equations , 1979 .

[6]  A. Griewank,et al.  Computation of cusp singularities for operator equations and their discretizations , 1989 .

[7]  Peter Kunkel.  A Tree-based analysis of a family of augmented systems for the computation of singular points , 1996 .

[8]  M. Hermann,et al.  Numerische Behandlung von Fortsetzungs- und Bifurkationsproblemen bei Randwertaufgaben , 1987 .

[9]  P. Kunkel.  Quadratically Convergent Methods for the Computation of Unfolded Singularities , 1988 .

[10]  W. Rheinboldt,et al.  The Role of the Tangent Mapping in Analyzing Bifurcation Behaviour , 1984 .

[11]  Alastair Spence,et al.  Non-simple Turning Points and Cusps , 1982 .

[12]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[13]  Martin Hermann,et al.  RWPKV: A software package for continuation and bifurcation problems in two-point boundary value problems , 1992 .

[14]  Wolf-Jürgen Beyn,et al.  Defining Equations for Singular Solutions and Numerical Applications , 1984 .

[15]  G. Reddien,et al.  Characterization and computation of singular points with maximum rank deficiency , 1986 .

[16]  Peter Kunkel,et al.  Continuation and collocation for parameter-dependent boundary value problems , 1989 .

[17]  H. Weber.  On the numerical approximation of secondary bifurcation problems , 1981 .

[18]  Klaus Böhmer,et al.  Resolving singular nonlinear equations , 1988 .

[19]  G. Moore,et al.  The numerical treatment of non-trivial bifurcation points , 1980 .