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Finite-Difference Methods for Boundary-Value Problems

  • H.-J. Reinhardt
Part of the Applied Mathematical Sciences book series (AMS, volume 57)

Abstract

In this chapter, we approximate by means of finite-differences several prototype examples of boundary-value problems in both ordinary and partial differential equations. For each individual problem, we develop one or more finite-difference schemes and state some results on the solvability of the associated (linear or non-linear) systems of equations. Then we formulate the original problem and its approximations as operator equations in suitable function spaces. In such a setting, we are then able to investigate accuracy properties of the finite-difference approximations themselves by analyzing the behavior of the truncation errors.

Keywords

Truncation Error Mesh Point Difference Quotient Order Ordinary Differential Equation Approximate Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Babuska, Prager & Vitasek (1966), Braun (1983), Ciariet, Schultz & Varga (1967)*, Coddington & Levinson (1955), Collatz (1966), Courant & Hilbert (1966), Forsythe & Wasow (1960), Garabedian (1964), Gladwell & Wait (1979), Hartman (1964), van der Houwen (1968), Isaacson & Keller (1966), John (1967,1982), Keller (1968, 1976), Mitchell & Griffiths (1980), Ortega & Rheinboldt (1970), Smirnow (1964), Smith (1978), Stoer & Bulirsch (1978), Stummel & Hainer (1982), Tömig (1979), Varga (1962), Wachspress (1966), Walter (1976)Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • H.-J. Reinhardt
    • 1
  1. 1.Fachbereich MathematikJohann-Wolfgang-Goethe-Universität6000 Frankfurt MainFederal Republic of Germany

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