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.


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  • [1] Fritz John, On integration of parabolic equations by difference methods. I. Linear and quasi-linear equations for the infinite interval, Comm. Pure Appl. Math. 5 (1952), 155–211. MR 0047885, https://doi.org/10.1002/cpa.3160050203
  • [2] R. P. Eddy, Stability in the numerical solution of initial value problems in partial differential equations, NOLM 10232, (1949)
  • [3] George G. O’Brien, Morton A. Hyman, and Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics 29 (1951), 223–251. MR 0040805
  • [4] Lipman Bers, On mildly nonlinear partial difference equations of elliptic type, J. Research Nat. Bur. Standards 51 (1953), 229–236. MR 0064291
  • [5] S. Gerschgorin, Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen, Z. Angew. Math. Mech. 10, 373-382 (1930)
  • [6] Eduard Batschelet, Über die numerische Auflösung von Ranswertproblemen bei elliptischen partiellen Differentialgleichungen, Z. Angew. Math. Physik 3 (1952), 165–193 (German). MR 0060912
  • [7] J. Gèvrey, Sur les équations aux derivées partielles du type parabolique, J. D. Math., Ser. 6, 9 (1913); 10 (1914)
  • [8] Pentti Laasonen, Über eine Methode zur Lösung der Wärmeleitungsgleichung, Acta Math. 81 (1949), 309–317 (German). MR 0032094, https://doi.org/10.1007/BF02395025

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

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