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Iterated deferred corrections for nonlinear boundary value problems

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References

  1. Ballester, C., andV. Pereyna: On the construction of discrete approximations to linear differential expressions. Math. Comp.21, 297–302 (1966).

    Google Scholar 

  2. Bayley, P., andP. Waltman: Existence and uniqueness of solutions of the first boundary value problem for non-linear second order differential equations. Arch. Rational Mech. Anal.21, 310–320 (1966).

    Google Scholar 

  3. Bulirsch, R., andJ. Stoer: Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus. Numer. Math.6, 413–427 (1964).

    Google Scholar 

  4. Ciarlet, P., M. Schultz, andR. Varga Numerical methods of higher accuracy for nonlinear boundary value problems I. Numer. Math.9, 394–431 (1967).

    Google Scholar 

  5. Collatz, L.: The numerical treatment of differential equations. Third Ed. Berlin-Göttingen-Heidelberg: Springer 1959

    Google Scholar 

  6. Daniel, J., V. Pereyna, andL. Schumaker: Iterated deferred corrections for initial value problems. MRC Tech. Report 808, University of Wisconsin, Madison (1967).

    Google Scholar 

  7. Hartman, P.: Ordinary differential equations. New York: Wiley 1964.

    Google Scholar 

  8. Henrici, P.: Discrete variable methods in ordinary differential equations. New York: Wiley 1962.

    Google Scholar 

  9. Householder, A.: Principles of numerical analysis. New York: McGraw-Hill 1953.

    Google Scholar 

  10. Lees, M., andM. Schultz: A Leray-Schauder principle forA-compact mappings and the numerical solution of non-linear two-point boundary value problems. In: Numerical solution of nonlinear differential equations (ed. by D. Greenspan) 167–180. New York: Wiley 1966.

    Google Scholar 

  11. Pereyna, V.: On improving an approximate solution of a functional equation by deferred corrections. Numer. Math.8, 376–391 (1966).

    Google Scholar 

  12. —— Accelerating the convergence of discretization algorithms. MRC Tech. Rep. 687, University of Wisconsin, Madison (1966). To appear in SIAM J. Numer. Anal.

    Google Scholar 

  13. —— Highly accurate discrete methods for nonlinear problems. Ph. D. Thesis, University of Wisconsin, Madison. Also MRC Tech. Rep. 749 (1967).

    Google Scholar 

  14. —— Iterated deferred corrections for nonlinear operator equations. MRC Tech. Rep. 763, University of Wisconsin, Madison (1967). Numer. Math.14, 316–323 (1967).

    Google Scholar 

  15. Urabe, M., andA. Reiter: Numerical computation of nonlinear forted oscillations by Galerkin's procedure. J. Math. Anal. Appl.14, 107–140 (1966).

    Google Scholar 

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Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-3 1-124-ARO-D-462.

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Pereyna, V. Iterated deferred corrections for nonlinear boundary value problems. Numer. Math. 11, 111–125 (1968). https://doi.org/10.1007/BF02165307

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