Global smooth solution curves using rigorous branch following

Jan Bouwe van den Berg; Jean Philippe Lessard; Konstantin Mischaikow

doi:10.1090/S0025-5718-10-02325-2

Global smooth solution curves using rigorous branch following

Jan Bouwe van den Berg, Jean Philippe Lessard, Konstantin Mischaikow

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46 Scopus citations

Abstract

In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators f : r{double-struck}^l1×B₁ → r{double-struck}^l2 ×B₂, where B₁ and B₂ are Banach spaces. The method is first introduced for parameter continuation and then generalized to pseudo-arclength continuation. Examples in the context of ordinary, partial and delay differential equations are given.

Original language	English (US)
Pages (from-to)	1565-1584
Number of pages	20
Journal	Mathematics of Computation
Volume	79
Issue number	271
DOIs	https://doi.org/10.1090/S0025-5718-10-02325-2
State	Published - Jul 2010

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-10-02325-2

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title = "Global smooth solution curves using rigorous branch following",

abstract = "In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators f : r{double-struck}l1×B1 → r{double-struck}l2 ×B2, where B1 and B2 are Banach spaces. The method is first introduced for parameter continuation and then generalized to pseudo-arclength continuation. Examples in the context of ordinary, partial and delay differential equations are given.",

author = "{van den Berg}, {Jan Bouwe} and Lessard, {Jean Philippe} and Konstantin Mischaikow",

year = "2010",

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T1 - Global smooth solution curves using rigorous branch following

AU - van den Berg, Jan Bouwe

AU - Lessard, Jean Philippe

AU - Mischaikow, Konstantin

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N2 - In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators f : r{double-struck}l1×B1 → r{double-struck}l2 ×B2, where B1 and B2 are Banach spaces. The method is first introduced for parameter continuation and then generalized to pseudo-arclength continuation. Examples in the context of ordinary, partial and delay differential equations are given.

AB - In this paper, we present a new method for rigorously computing smooth branches of zeros of nonlinear operators f : r{double-struck}l1×B1 → r{double-struck}l2 ×B2, where B1 and B2 are Banach spaces. The method is first introduced for parameter continuation and then generalized to pseudo-arclength continuation. Examples in the context of ordinary, partial and delay differential equations are given.

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DO - 10.1090/S0025-5718-10-02325-2

M3 - Article

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SP - 1565

EP - 1584

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 271

ER -

Global smooth solution curves using rigorous branch following

Abstract

All Science Journal Classification (ASJC) codes

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