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

Butcher, J. C.; Cash, J. R.; Moore, G.; Russell, R. D.

doi:10.1090/S0025-5718-1995-1284662-1

Defect correction for two-point boundary value problems on nonequidistant meshes
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by J. C. Butcher, J. R. Cash, G. Moore and R. D. Russell PDF

Math. Comp. 64 (1995), 629-648 Request permission

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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