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Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations pp 374–407Cite as

Use of Green's functions in the numerical solution of two-point boundary value problems

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 362))

Abstract

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

Supported by the National Aeronautics and Space Administration — Washington, D.C.

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Authors and Affiliations

  1. Rich Electronic Computer Center, Georgia Institute of Technology, Atlanta, Georgia

    L. J. Gallaher & I. E. Perlin

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  1. L. J. Gallaher
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  2. I. E. Perlin
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Dale G. Bettis

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© 1974 Springer-Verlag

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Gallaher, L.J., Perlin, I.E. (1974). Use of Green's functions in the numerical solution of two-point boundary value problems. In: Bettis, D.G. (eds) Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations. Lecture Notes in Mathematics, vol 362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066602

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  • DOI: https://doi.org/10.1007/BFb0066602

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06602-6

  • Online ISBN: 978-3-540-37911-9

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