Abstract
A numerical method is developed for approximating the exact solution of an operator equation on a certain finite grid to within a desired tolerance. The method incorporates discretizations which admit asymptotic expansions of the error, mesh refinement strategies and discrete Newton methods. An algorithm is given in which essentially the largest adequate mesh size is used. A homotopy method for obtaining good starting values for a Newton-type method applied to a coarse grid discretization and the connection that our approach has with multigrid methods are discussed. Numerical examples for two-point boundary value problems and elliptic boundary value problems are given.
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Allgower, E.L., Böhmer, K., Mc Cormick, S. (1981). Discrete correction methods for operator equations. In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090676
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DOI: https://doi.org/10.1007/BFb0090676
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