Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the integration of non-linear parabolic equations by implicit difference methods

Author: Milton E. Rose
Journal: Quart. Appl. Math. 14 (1956), 237-248
MSC: Primary 65.3X
DOI: https://doi.org/10.1090/qam/85610
MathSciNet review: 85610
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Abstract: The object of this paper is to investigate how solutions of mixed initial-boundary value problems for a certain class of non-linear parabolic equations may be obtained by solving suitable implicit difference equations on a rectangular lattice and taking the limit of such solutions as the mesh of the lattice tends to zero.

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

  • [1] F. John, On integration of parabolic equations by difference methods, Communs. on Pure and Appl. Math. 5, 155-211 (1952) MR 0047885
  • [2] R. P. Eddy, Stability in the numerical solution of initial value problems in partial differential equations, NOLM 10232, (1949)
  • [3] G. G. O'Brien, M. A. Hyman, S. Kaplan, A study of the numerical solution of partial differential equations, J. Math. Phys. 29, 223-251 (1951) MR 0040805
  • [4] L. Bers, On mildly non-linear partial difference equations of elliptic type, J. Research Natl. Bur. Standards (1953) MR 0064291
  • [5] S. Gerschgorin, Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen, Z. Angew. Math. Mech. 10, 373-382 (1930)
  • [6] E. Batchelet, Über die numerische Auflösung von Randwertproblemen bei elliptischen partiellen Differentialgleichungen, ZAMP, 3, 165-193 (1952) MR 0060912
  • [7] J. Gèvrey, Sur les équations aux derivées partielles du type parabolique, J. D. Math., Ser. 6, 9 (1913); 10 (1914)
  • [8] P. Laasonen, Über eine Methode zur Lösung der Wärmeleitungsgleichung, Acta Mathematica, 81 (1949) MR 0032094

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DOI: https://doi.org/10.1090/qam/85610
Article copyright: © Copyright 1956 American Mathematical Society

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