Defect Corrections via Neighbouring Problems. I. General Theory.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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This document solves Fy 0 numerically using two different methods, the first of which is sketched already and the second introducing a neighbouring problem N.P. Fu d, absolute value of d small, with known solution. One solves the original problem and the N.P. with the same discretization method. The known error of the N.P. is used as an estimation for the unknown error of the original problem. These procedures are used iteratively and their relations are discussed. In subsequent papers the general theory will be applied to some special cases and will discuss relations to collocation methods and to PEREYRAs deferred correction methods.
- Theoretical Mathematics