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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Tensor product analysis of partial difference equations


Authors: R. E. Lynch, J. R. Rice and D. H. Thomas
Journal: Bull. Amer. Math. Soc. 70 (1964), 378-384
DOI: https://doi.org/10.1090/S0002-9904-1964-11105-8
MathSciNet review: 0169390
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  • 1. G. A. Baker, Jr. and T. A. Oliphant, An implicit, numerical method for solving the two-dimensional heat equation, Quart. Appl. Math. 17 (1960), 361-373. MR 110207
  • 2. G. Birkhoff and R. S. Varga, Implicit alternating direction methods, Trans. Amer. Math. Soc. 92 (1959), 13-24. MR 105814
  • 3. G. Birkhoff, R. S. Varga and D. M. Young, Alternating direction implicit methods, Advances in Computers, Vol. III, pp. 189-273, Academic Press, New York, 1962. MR 168131
  • 4. S. D. Conte and R. T. Dames, An alternating direction method for solving the biharmonic equation, Math. Comp. 12 (1958), 198-205. MR 105813
  • 5. Jim Douglas, Alternating direction methods for three space variables, Numer. Math. 4 (1962), 41-63. MR 136083
  • 6. Jim Douglas, Jr. and H. H. Rachford, Jr., On the numerical solution of heat conduction problems in two or three space variables, Trans. Amer. Math. Soc. 82 (1956), 421-439. MR 84194
  • 7. C. de Boor, and J. R. Rice, Chebyshev approximation by αII(x - r)/(x + s) and application to ADI iteration, J. Soc. Indust. Appl. Math. 11 (1963), 159-169. MR 161461
  • 8. P. R. Halmos, Finite-dimensional vector spaces, Chapter II, Van Nostrand, Princeton, N. J., 1958. MR 89819
  • 9. D. W. Peaceman and H. H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math. 3 (1955), 28-41. MR 71874
  • 10. R. S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 158502
  • 11. H. O. Cordes, Separation der Variablen in Hilbertschen Räumen, Math. Ann. 125 (1953), 401-434. MR 55582
  • 12. B. Friedman, An abstract formulation of the method of separation of variables, Proceedings of the conference on differential equations (dedicated to A. Weinstein), pp. 209-226, Univ. of Maryland Book Store, 1956. MR 82638
  • 13. E. Egerváry, Über eine Methode zur numerischen Lösung der Poissonschen Differenzengleichung für beliebige Gebiete, Acta Math. Acad. Sci. Hungar. 11 (1960), 341-361. MR 136526
  • 14. J. Heller, Simultaneously, successive, and alternating direction iteration schemes, J. Soc. Indust. Appl. Math. 8 (1960), 150-173. MR 121978


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1964-11105-8

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