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Spline-galerkin methods for initial-value problems with variable coefficients

Part of the Lecture Notes in Mathematics book series (LNM,volume 363)

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References

  1. Thomée, V., Convergence estimates for semi-discrete Galerkin methods for initial value problems, Numerische, insbesondre approximations-theoretische, Behandung von Functionalgleichungen, Springer Lecture Notes, to appear.

    Google Scholar 

  2. Thomée, V., and Wendroff, B., "Convergence estimates for Galerkin methods for variable coefficient initial-value problems," to appear SIAM J. Numer. Anal.

    Google Scholar 

  3. Wendroff, B., "On finite elements for equations of evolution," Los Alamos Scientific Laboratory Report No. LA-DC-72-1220, 1972.

    Google Scholar 

Bibliography

  1. Axelsson, O. "A generalized SSOR method," BIT 13, 443–467 (1972).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Birkhoff, G., Varga, R. S., and Young, D. "Alternating direction implicit methods," Advances in Computers, Vol. 3, 189–273 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Concus, Paul, and Golub, Gene H. "Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations," Report STAN-CS-72-278, Computer Science Department, Stanford University, April 1972.

    Google Scholar 

  4. Dupont, Todd. "A factorization procedure for the solution of elliptic difference equations," SIAM J. Numer. Anal. 5, 753–782 (1968).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Dupont, Todd, Kendall, Richard P., and Rachford, H.H., Jr. "Approximate factorization procedure for solving self-adjoint elliptic difference equations," SIAM J. Numer. Anal. 5, 559–573 (1968).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Ehrlich, L. W. "The Block Symmetric Successive Overrelaxation Method," doctoral thesis, University of Texas, Austin (1963).

    MATH  Google Scholar 

  7. Ehrlich, L. W. "The block symmetric successive overrelaxation method," J. Soc. Indust. Appl. Math. 12, 807–826 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Evans, D. J., and Forrington, C. V. D. "An iterative process for optimizing symmetric overrelaxation," Comput. J. 6, 271–273 (1963).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Golub, G. H., and Varga, R. S. "Chebyshev semi-iterative methods, successive, overrelaxation iterative methods, and second-order Richardson iterative methods," Numer. Math., Parts I and II 3, 147–168 (1961).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Habetler, G. J., and Wachspress, E. L. "Symmetric successive overrelaxation in solving diffusion difference equations," Math. Comp. 15, 356–362 (1961).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Peaceman, D. W., and Rachford, H. H., Jr. "The numerical solution of parabolic and elliptic differential equations," J. Soc. Indus. Appl.Math. 3, 28–41 (1955).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Sheldon, J. "On the numerical solution of elliptic difference equations," Math. Tables Aids Comput. 9, 101–112 (1955).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Stone, H. L. "Iterative solution of implicit approximation of multidimensional partial differential equations," SIAM J. Numer. Anal. 5, 530–558 (1968).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Varga, R. S. "A comparison of the successive overrelaxation method and semi-iterative methods using Chebyshev polynomials," J. Soc. Indus. Appl. Math. 5, 39–46 (1957).

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Widlund, O. B. "On the rate of convergence of an alternating direction implicit method in a noncommutative case," Math. Comp. 20, 500–515 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Young, D. M. "On the solution of linear systems by iteration," Proc. Sixth Symp. in Appl. Math. Amer. Math. Soc. VI, McGraw-Hill, New York, 283–298 (1956).

    Google Scholar 

  17. Young, D. M. "A bound on the optimum relaxation factor for the successive overrelaxation method," Numer. Math. 16, 408–413 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Young, D. M. "Second-degree iterative methods for the solution of large linear systems," J. Approx. Theory 5, 137–148 (1972).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Young, D. M. Iterative Solution of Large Linear Systems, Academic Press, New York, 1971.

    MATH  Google Scholar 

  20. Young, D. M. "On the accelerated SSOR method for solving large linear systems," to appear.

    Google Scholar 

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Wendroff, B. (1974). Spline-galerkin methods for initial-value problems with variable coefficients. In: Watson, G.A. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069137

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  • DOI: https://doi.org/10.1007/BFb0069137

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