Separable parameterized equations, static bifurcation points, extended systems, Newton's method, LU factorization, curve switching and tracking
Many applications give rise to separable parameterized equations, which have the form A(y, µ)z + b(y, µ) = 0, where z ∈ RN , y ∈ Rn, µ ∈ Rs, and the (N + n) × N matrix A(y, µ) and (N + n) vector b(y, µ) are C2 -Lipschitzian in (y, µ) ∈ Ω ⊂ Rn × Rs. We present a technique which reduces the original equation to the form f (y, µ) = 0, where f : Ω → Rn is C2 -Lipschitzian in (y, µ). This reduces the dimension of the space within which the bifurcation relation occurs. We derive expressions required to implement methods to solve the reduced equation. Numerical examples illustrate the use of the technique.
Electronic Transactions on Numerical Analysis
Required Publisher's Statement
Copyright 2009, Kent State University. ISSN 1068-9613
Shen, Yun-Qiu and Ypma, Tjalling, "Numerical Bifurcation of Separable Parameterized Equations" (2009). Mathematics. 91.
Subjects - Topical (LCSH)
Singular value decomposition; Separable algebras; Bifurcation theory; Differential equations, Nonlinear; Newton-Raphson method
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