A modified simple shooting method for solving two-point boundary-value problems

Raymond Holsapple; Ram Venkataraman; David Doman

doi:10.1109/AERO.2003.1235204

A modified simple shooting method for solving two-point boundary-value problems

Raymond Holsapple, Ram Venkataraman, David Doman

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

33 Scopus citations

Abstract

In the study of mechanics and optimal control, one often encounters what is called a two-point boundary-value problem (TPBVP). A couple of methods exist for solving these problems, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM). In this paper a new method is proposed that was designed from the favorable aspects of both the SSM and the MSM. The Modified Simple Shooting Method (MSSM) sheds undesirable aspects of both previously mentioned methods to yield a superior, faster method for solving TPBVPs. The convergence of the MSSM is proven under mild conditions on the TPBVP. A comparison of the MSM and the MSSM is made for a problem where both methods converge. We also provide a second example where the MSM fails to converge while the MSSM converges rapidly.

Original language	English
Title of host publication	2003 IEEE Aerospace Conference, Proceedings
Pages	2783-2790
Number of pages	8
DOIs	https://doi.org/10.1109/AERO.2003.1235204
State	Published - 2003
Event	2003 IEEE Aerospace Conference - Big Sky, MT, United States Duration: Mar 8 2003 → Mar 15 2003

Publication series

Name	IEEE Aerospace Conference Proceedings
Volume	6
ISSN (Print)	1095-323X

Conference

Conference	2003 IEEE Aerospace Conference
Country/Territory	United States
City	Big Sky, MT
Period	03/8/03 → 03/15/03

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10.1109/AERO.2003.1235204

Cite this

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title = "A modified simple shooting method for solving two-point boundary-value problems",

abstract = "In the study of mechanics and optimal control, one often encounters what is called a two-point boundary-value problem (TPBVP). A couple of methods exist for solving these problems, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM). In this paper a new method is proposed that was designed from the favorable aspects of both the SSM and the MSM. The Modified Simple Shooting Method (MSSM) sheds undesirable aspects of both previously mentioned methods to yield a superior, faster method for solving TPBVPs. The convergence of the MSSM is proven under mild conditions on the TPBVP. A comparison of the MSM and the MSSM is made for a problem where both methods converge. We also provide a second example where the MSM fails to converge while the MSSM converges rapidly.",

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AU - Venkataraman, Ram

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AB - In the study of mechanics and optimal control, one often encounters what is called a two-point boundary-value problem (TPBVP). A couple of methods exist for solving these problems, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM). In this paper a new method is proposed that was designed from the favorable aspects of both the SSM and the MSM. The Modified Simple Shooting Method (MSSM) sheds undesirable aspects of both previously mentioned methods to yield a superior, faster method for solving TPBVPs. The convergence of the MSSM is proven under mild conditions on the TPBVP. A comparison of the MSM and the MSSM is made for a problem where both methods converge. We also provide a second example where the MSM fails to converge while the MSSM converges rapidly.

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Y2 - 8 March 2003 through 15 March 2003

ER -

A modified simple shooting method for solving two-point boundary-value problems

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