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A variable order finite difference method for nonlinear multipoint boundary value problems


Authors: M. Lentini and V. Pereyra
Journal: Math. Comp. 28 (1974), 981-1003
MSC: Primary 65L10
DOI: https://doi.org/10.1090/S0025-5718-1974-0386281-4
MathSciNet review: 0386281
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Abstract: An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order to achieve a required tolerance. Extensive numerical experimentation and a FORTRAN program are included.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0386281-4
Keywords: Adaptive finite difference method, variable order method, nonlinear multipoint boundary value problem, first order systems boundary problem
Article copyright: © Copyright 1974 American Mathematical Society

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