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Numerical methods and existence theorems for parabolic differential equations whose coefficients are singular on the boundary


Author: Pierre Jamet
Journal: Math. Comp. 22 (1968), 721-743
MSC: Primary 65.68
MathSciNet review: 0255084
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  • [1] R. Courant, K. Friedrichs, and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928), no. 1, 32–74 (German). MR 1512478, 10.1007/BF01448839
  • [2] C. W. Cryer, The difference analogue of Gauss’ theorem, SIAM J. Numer. Anal. 4 (1967), 155–162. MR 0213763
  • [3] C. W. Cryer, "On difference approximations to elliptic partial differential equations in $ {R^n}$." (To appear.)
  • [4] Dennis Eisen, The equivalence of stability and convergence for finite difference schemes with singular coefficients, Numer. Math. 10 (1967), 20–29. MR 0214295
  • [5] P. Jamet, Numerical Methods and Existence Theorems for Singular Linear BoundaryValue Problems, Doctoral Thesis, Univ. of Wisconsin, Madison, Wis., 1967.
  • [6] Pierre Jamet and Seymour V. Parter, Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary, SIAM J. Numer. Anal. 4 (1967), 131–146. MR 0215543
  • [7] J. J. Kohn and L. Nirenberg, Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math. 20 (1967), 797–872. MR 0234118
  • [8] W. V. Koppenfels, Über die Existenz der Lösungen linearer partieller Differentialgleichungen vom elliptischen Typus, Dissertation, Göttingen, 1929.
  • [8'] Heinz-Otto Kreiss and Einar Lundqvist, On difference approximations with wrong boundary values, Math. Comp. 22 (1968), 1–12. MR 0228193, 10.1090/S0025-5718-1968-0228193-X
  • [9] Seymour V. Parter, Numerical methods for generalized axially symmetric potentials, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 500–516. MR 0191113
  • [9'] Seymour V. Parter, Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem, Numer. Math. 4 (1962), 277–292. MR 0148232
  • [10] P. Raviart, Sur l'Approximation de Certaines Équations d'Évolution Linéaires et Non Linéaires, Doctoral Thesis, Paris, 1965.
  • [11] Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957. MR 0093918
  • [12] S. L. Sobolev, Applications of functional analysis in mathematical physics, Translated from the Russian by F. E. Browder. Translations of Mathematical Monographs, Vol. 7, American Mathematical Society, Providence, R.I., 1963. MR 0165337

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DOI: https://doi.org/10.1090/S0025-5718-1968-0255084-0
Article copyright: © Copyright 1968 American Mathematical Society