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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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