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Convergence of difference methods for initial and boundary value problems with discontinuous data

Authors: Bruce Chartres and Robert Stepleman
Journal: Math. Comp. 25 (1971), 729-732
MSC: Primary 65L10
MathSciNet review: 0303739
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Abstract: This paper extends the classical convergence theory for numerical solutions to initial and boundary value problems with continuous data (the right-hand side) to problems with Riemann integrable data. Order of convergence results are also obtained.

References [Enhancements On Off] (What's this?)

  • [1] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • [2] Germund Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations, Kungl. Tekn. Högsk. Handl. Stockholm. No. 130 (1959), 87. MR 0102921
  • [3] R. Goodman, Round-Off Error in the Numerical Solution of Retarded Ordinary Differential Equations, Thesis, Harvard University, Cambridge, Mass., 1971.
  • [4] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
  • [5] Peter Henrici, Error propagation for difference method, John Wiley and Sons, Inc., New York-London, 1963. MR 0154416
  • [6] Milton Lees, Discrete methods for nonlinear two-point boundary value problems, Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965) Academic Press, New York, 1966, pp. 59–72. MR 0202323
  • [7] T. S. Zverkina, Approximate solution of differential equations with retarded argument and differential equations with discontinuous right-hand sides, Trudy Sem. Teor. Differencial. Uravneniĭ s Otklon. Argumentom Univ. Družby Narodov Patrisa Lumumby 1 (1962), 76–93 (Russian). MR 0185239

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Keywords: Convergence, Euler's method, difference method, discontinuous data, boundary value
Article copyright: © Copyright 1971 American Mathematical Society

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