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Mathematics of Computation

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Defect correction for two-point boundary value problems on nonequidistant meshes


Authors: J. C. Butcher, J. R. Cash, G. Moore and R. D. Russell
Journal: Math. Comp. 64 (1995), 629-648
MSC: Primary 65L10; Secondary 65L12
DOI: https://doi.org/10.1090/S0025-5718-1995-1284662-1
MathSciNet review: 1284662
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Abstract: New finite difference formulae of arbitrary order are derived for the special class of second-order two-point boundary value problems $ y'' = f(x,y(x)), a \leq x \leq b$ . Variable mesh spacing is possible, and the required accuracy is achieved under a very mild mesh condition. A natural defect correction framework is set up to compute the higher-order approximations.


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DOI: https://doi.org/10.1090/S0025-5718-1995-1284662-1
Article copyright: © Copyright 1995 American Mathematical Society