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    Solution of Nonlinear Two-Point Boundary Value Problems by Linear Programming

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    TR1.pdf (2.606Mb)
    Date
    1967
    Author
    Rosen, J.B.
    Meyer, Robert
    Publisher
    University of Wisconsin-Madison Department of Computer Sciences
    Metadata
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    Abstract
    A system of n nonlinear ordinary differential equations is considered on the interval [a, b] with at least one of the n boundary conditions specified at each end of the interval. In addition, any available a priori bounds on the solution vector may be imposed. An iterative method for solution is described which is essentially a Newton-Raphson method with a linear programming solution at each iteration. Every iterate is a minimax solution to a linearized finite difference approximation to the original system, and also satisfies the boundary conditions and the a priori bounds. The method will always converge at least as fast as Newton-Raphson, and may converge when Newton-Raphson fails. A number of computational examples are described.
    Permanent Link
    http://digital.library.wisc.edu/1793/57454
    Citation
    TR1
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    • CS Technical Reports

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