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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


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
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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PII: S 0025-5718(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