Numerical continuation of solution at a singular point of high codimension for systems of nonlinear algebraic or transcendental equations

DOI10.1134/S0965542516090104zbMath1361.65032MaRDI QIDQ519687

E. B. Kuznetsov, Sergey D. Krasnikov

Publication date: 5 April 2017

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

algorithmnumerical examplescontinuation methodsingular pointcodimensionLyapunov-Schmidt reductionsystembifurcation equationsimple bifurcation pointLevin's methodnonlinear algebraic and transcendental equations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)

Related Items

Passage through limiting singular points by applying the method of solution continuation with respect to a parameter in inelastic deformation problems

Uses Software

• UNCMND
• pchip

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical continuation of solution at singular points of codimension one
• Optimal parametrization in numerical construction of curve
• Parametrization of a solution at bifurcation points
• Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact
• A remark on the parametrization of the numerical solution of boundary value problems
• Numerical methods in bifurcation problems. Lectures delivered at the Indian Institute of Science, Bangalore, under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics. Notes by A. K. Nandakumaran and Mythily Ramaswamy
• Bifurcation theory. An introduction with applications of PDEs
• A parametric approximation
• The best parameterization for parametric interpolation
• Bifurcation from simple eigenvalues
• Continuation of solutions in multiparameter approximation of curves and surfaces
• Multidimensional parametrization and numerical solution of systems of nonlinear equations
• Numerical continuation of the solution at bifurcation points of mathematical models
• A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces