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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Stability of bounded solutions of linear functional equations
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by Joel N. Franklin PDF
Math. Comp. 25 (1971), 413-424 Request permission

Abstract:

The weak sequential compactness of reflexive Banach spaces is used to explain the fact that certain ill-posed, linear problems become well-posed if the solutions are required to satisfy a prescribed bound. Applications are made to the computability of solutions of ill-posed problems associated with elliptic and parabolic partial differential equations.
References
    J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale Univ. Press, New Haven, Conn., 1923.
  • Fritz John, Numerical solution of the equation of heat conduction for preceding times, Ann. Mat. Pura Appl. (4) 40 (1955), 129–142. MR 87224, DOI 10.1007/BF02416528
  • Fritz John, Numerical solution of problems which are not well posed in the sense of Hadamard, Symposium on the numerical treatment of partial differential equations with real characteristics: Proceedings of the Rome Symposium (28-29-30 January 1959) organized by the Provisional International Computation Centre Libreria Eredi Virgilio Veschi, Rome, 1959, pp. 103–116. MR 0107983
  • Fritz John, Continuous dependence on data for solutions of partial differential equations with a presribed bound, Comm. Pure Appl. Math. 13 (1960), 551–585. MR 130456, DOI 10.1002/cpa.3160130402
  • L. E. Payne, On some non well posed problems for partial differential equations, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966) John Wiley & Sons, Inc., New York, N.Y., 1966, pp. 239–263. MR 0213749
  • Robert D. Richtmyer, Difference methods for initial-value problems, Interscience Tracts in Pure and Applied Mathematics, Tract 4, Interscience Publishers, Inc., New York, 1957. MR 0093918
  • Frédéric Riesz and Béla Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1953 (French). 2ème éd. MR 0056821
  • P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
  • J. R. Cannon, Some numerical results for the solution of the heat equation backwards in time, Numerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966) John Wiley & Sons, Inc., New York, N.Y., 1966, pp. 21–54. MR 0207221
  • Jim Douglas Jr., Approximate continuation of harmonic and parabolic functions, Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965) Academic Press, New York, 1966, pp. 353–364. MR 0202333
  • Richard Saylor, Numerical elliptic continuation, SIAM J. Numer. Anal. 4 (1967), 575–581. MR 222461, DOI 10.1137/0704052
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 413-424
  • MSC: Primary 47A50; Secondary 35R25
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0380461-7
  • MathSciNet review: 0380461