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Initial-value methods for boundary-value problems

In: Numerical Solution of Ordinary Differential Equations

Author

Listed:
  • L. Fox

    (Oxford University)

  • D. F. Mayers

    (Oxford University)

Abstract

As we saw in Chapter 1, a boundary-value problem is one in which conditions associated with the differential equations are specified at more than one point. Here we shall concentrate on the existence of just two boundary points, which is the most usual case. We may be interested in a single differential equation of nth order, or a set of lower-order equations equivalent to this, a special case of which is a simultaneous set of n first-order equations. In all cases there will be n associated conditions, the boundary conditions, either separated or unseparated. In the separated case there will be p conditions at one boundary point and q at the other, where p + q = n, and in the unseparated case at least some of the n conditions will involve combinations of the values of the functions or their derivatives at both boundary points.

Suggested Citation

  • L. Fox & D. F. Mayers, 1987. "Initial-value methods for boundary-value problems," Springer Books, in: Numerical Solution of Ordinary Differential Equations, chapter 5, pages 98-127, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3129-9_5
    DOI: 10.1007/978-94-009-3129-9_5
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