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Shooting Methods for Linear Boundary Value Problems

In: A First Course in Ordinary Differential Equations

Author

Listed:
  • Martin Hermann

    (Friedrich Schiller University, Institute of Applied Mathematics)

  • Masoud Saravi

    (Islamic Azad University Nour Branch, Department of Mathematics)

Abstract

The final Chap. 8 deals with shooting methods for the solution of linear two-point boundary value problems. After the definition of a two-point boundary value problem and the classification of the boundary conditions in separated, non-separated, and partially separated conditions, the simple shooting method is presented. Then, the method of complementary functions is derived from the simple shooting method under the assumption that the boundary conditions are partially separated. The discussion of the stability of the simple shooting method and the method of complementary functions shows that these techniques have to be improved. The corresponding (improved) segmented methods are the multiple shooting method and the stabilized march method. Both methods are described in detail. Their better stability behavior is shown.

Suggested Citation

  • Martin Hermann & Masoud Saravi, 2014. "Shooting Methods for Linear Boundary Value Problems," Springer Books, in: A First Course in Ordinary Differential Equations, edition 127, chapter 0, pages 241-277, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1835-7_8
    DOI: 10.1007/978-81-322-1835-7_8
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