A Method for the Numerical Determination of Bifurcation States of Nonlinear Systems of Equations
- 1 June 1975
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 12 (3), 439-451
- https://doi.org/10.1137/0712034
Abstract
A numerical technique is presented for determining a simple turning point in a branch of solutions of an algebraic system of equations depending on a scalar parameter. Results are given from testing the method on discrete versions of several mildly nonlinear boundary value problems to determine turning points in the positive solution branch.Keywords
This publication has 12 references indexed in Scilit:
- Existence and error estimates for solutions of a discrete analog of nonlinear eigenvalue problemsMathematics of Computation, 1972
- Finite Difference Methods for Mildly Nonlinear Eigenvalue ProblemsSIAM Journal on Numerical Analysis, 1971
- Axisymmetric buckling of hollow spheres and hemispheresCommunications on Pure and Applied Mathematics, 1970
- Approximate Solution and Error Bounds for Quasi-Linear Elliptic Boundary Value ProblemsSIAM Journal on Numerical Analysis, 1970
- Nonlinear diffusion induced by nonlinear sourcesQuarterly of Applied Mathematics, 1970
- Eigenfunction Branches of Nonlinear Operators, and their BifurcationsLecture Notes in Mathematics, 1969
- Accelerating the Convergence of Discretization AlgorithmsSIAM Journal on Numerical Analysis, 1967
- Convergence of the newton process to multiple solutionsNumerische Mathematik, 1966
- An extension of the Newton-Kantorovič method for solving nonlinear equations with an application to elasticityJournal of Mathematical Analysis and Applications, 1966
- Mildly nonlinear elliptic partial differential equations and their numerical solution. INumerische Mathematik, 1965