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On certain iterative methods for solving nonlinear difference equations

  • E. G. D'Jakonov
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 109)

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References

  1. 1.
    Vishik, M.I. Quasilinear strongly elliptic systems of differential equations, having divergent form. Trudi Moskovskogo Matematioheskogo Obshestva, 12, 1963, pp.129–184. (Russian)Google Scholar
  2. 2.
    Nirenberg, L. Remarks on strongly elliptic partial differential equations. Comm. on Pure and Appl. Math., v.VIII, (1955), 648–674.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Douglas, J. Alternating direction iteration method for mildly nonlinear elliptic difference equations. Numer. Math., v.3, (1961), N 1, 92–98.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wachspress, E.L. Extended application of alternating direction implicit iteration model problem theory. J. Soc. Industr. and Appl. Math., v.11, (1963), N 3, 994–1016.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gunn, J.E. The numerical solution of by a semi-explicit alternating direction iterative technique. Numer. Math., v.6 (1964), N 3, 181–184.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gunn, J.E. On the two-stage iterative method Douglas for mildly nonlinear elliptic difference equations. Numer. Math., v.6, (1964), N 3, 243–249.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gunn, J.E. The solution of elliptic difference equations by semi-explicit iterative technique. J. Soc. Industr. and Appl. Math., v.2, (1965), N 1, 24–45.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    D'Jakonov, E.G. On one iterative method for solving difference equations. Dokl. A.N. SSSR, 138, (1961), 522–525. (Russian)MathSciNetGoogle Scholar
  9. 9.
    D'Jakonov, E.G. The application of operators equivalent with respect to spectrum in solving difference analogues of strongly elliptic systems. Dokl. A.N.SSSR, 163, (1965), 1105–1109.MathSciNetGoogle Scholar
  10. 10.
    D'Jakonov, E.G. On construction of iterative methods on the base of using operators equivalent with respect to spectrum. Z. Vyoisl. Mat. i Mat. Fiz., 6, (1966), N 1, 12–34; N 4, 777–778. (Russian)MathSciNetGoogle Scholar
  11. 11.
    D'Jakonov, E.G. On convergence of the certain iterative method. Uspechy Mat. Nauk, 21, 1966, N 1, 181–183. (Russian)MathSciNetGoogle Scholar
  12. 12.
    Kantorovich, L.V., Akilov, G.P. Functional Analysis in Normed Spaces, Fizmatgiz, Moscow, 1959. (Russian)zbMATHGoogle Scholar
  13. 13.
    Koshelev, A.I. On the convergence of the method of successive approximations for quasilinear elliptic equations. Dokl. Akad. Nauk SSSR, 142, (1962), 1007–1010.MathSciNetGoogle Scholar
  14. 14.
    Jakovlev, M.I. On certain methods of solving nonlinear equations. Trudi Matematicheskogo Instituta imeni V.A. Steklova, v.84, (1965), 8–40. (Russian)MathSciNetGoogle Scholar
  15. 15.
    Petryshin, W.V. Direct and iterative methods for the solution of linear operator equations in Hilbert space. Trans. Amer. Math. Soc., v.105, (1962), 136–175.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Petryshin, W.V. On the extension and the solution of nonlinear operator equations. Illinois J. Math., v.10, (1966), N 2, 255–274.MathSciNetGoogle Scholar
  17. 17.
    D'Jakonov, E.G. On certain difference schemes for solving boundary value problems. Z. Vycial. Mat. i Mat. Fiz., v.2, (1962), 57–79, 511.MathSciNetGoogle Scholar
  18. 18.
    Douglas, J. Alternating direction methods for three space variables. Numer. Math., 4, (1962), N 1, 43–63.MathSciNetzbMATHGoogle Scholar
  19. 19.
    D'Jakonov, E.G. Difference schemes with a disintegrating operator for multidimensional problems. Z. Vycial. Mat. i Mat. Fiz., v.4, (1963), 581–607. (Russian)Google Scholar
  20. 20.
    Melvyn S. Berger. On von Karman's equations and the buckling of a thin elastic plate. Comm. Pure and Appl. Math., 20, (1967), N 4, 687–719.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Hockney, R.W. A fast direct solution of Poissons equation using Fourier analysis. J. Assoc. Comp. Mach., v.12, (1965), N 1, 95–113.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Cooley, J.W., Tukey, J.W. An algorithm for the machine calculation of complex Fourier series. Math. Comp., v.19, 1965, 297–301.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    D'Jakonov, E.G. On the application of disintegrating difference operators. Z. Vicisl. Mat. i Mat. Fiz., 3, (1963), 385–388.MathSciNetGoogle Scholar

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© Springer-Verlag 1969

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  • E. G. D'Jakonov

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