The Calculation of Turning Points of Nonlinear Equations
Authors:
- G. MooreGMG. Moore
- A. SpenceASA. Spence
- 1 August 1980
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 17 (4) , 567-576
Abstract
This paper is concerned with the determination of a type of singular point, called a “turning” or “limit” point, of nonlinear equations depending on a parameter. An enlarged system is introduced for which the turning point is a nonsingular solution and thus standard methods can be used to compute it. An efficient implementation of Newton’s method in the finite-dimensional case is presented and numerical results for discretizations of a differential equation and an integral equation are given.Keywords
This publication has 12 references indexed in Scilit:
- Numerical computation of branch points in ordinary differential equationsNumerische Mathematik, 1979
- Iterative bounds for the stable solutions of convex non-linear boundary value problemsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1977
- Solution of nonlinear boundary value problems—IX. Evaluation of branching points based on the differentiation with respect to boundary conditionsChemical Engineering Science, 1975
- Bifurcation in Nonlinear Hydrodynamic StabilitySIAM Review, 1975
- A Method for the Numerical Determination of Bifurcation States of Nonlinear Systems of EquationsSIAM Journal on Numerical Analysis, 1975
- Algorithms for the Nonlinear Eigenvalue ProblemSIAM Journal on Numerical Analysis, 1973
- Perturbed bifurcation theoryArchive for Rational Mechanics and Analysis, 1973
- The Application of Newton’s Method to the Problem of Elastic StabilityJournal of Applied Mechanics, 1972
- Approximate Solution of Operator Equations1972
- The solution of characteristic value-vector problems by Newton's methodNumerische Mathematik, 1968