A double shooting scheme for certain unstable and singular boundary value problems

Alvin Bayliss

doi:10.1090/S0025-5718-1978-0464598-6

A double shooting scheme for certain unstable and singular boundary value problems

Alvin Bayliss^*

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article

5 Scopus citations

Abstract

A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.

Original language	English (US)
Pages (from-to)	61-71
Number of pages	11
Journal	Mathematics of Computation
Volume	32
Issue number	141
DOIs	https://doi.org/10.1090/S0025-5718-1978-0464598-6
State	Published - Jan 1978

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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title = "A double shooting scheme for certain unstable and singular boundary value problems",

abstract = "A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.",

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AB - A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.

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