Discrete correction methods for operator equations

  • E. L. Allgower
  • K. Böhmer
  • S. Mc Cormick
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 878)


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.


Asymptotic Expansion Multigrid Method Homotopy Method Richardson Extrapolation Nonlinear Elliptic Boundary 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • E. L. Allgower
    • 1
  • K. Böhmer
    • 2
  • S. Mc Cormick
    • 1
  1. 1.Mathematics DepartmentColorado State UniversityFort CollinsUSA
  2. 2.Fachbereich MathematikUniversität MarburgMarburg

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