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Global codes for BVODEs and their comparison

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Numerical Integration of Differential Equations and Large Linear Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 968))

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§VI. References

  1. U. Ascher, J. Christiansen and R.D. Russell, A collocation solver for mixed order systems of boundary value problems. Math. Comp. 33 (1978), 659–679.

    Article  MathSciNet  MATH  Google Scholar 

  2. U. Ascher, J. Christiansen and R.D. Russell, COLSYS-A collocation code for boundary value problems, 1979, in codes for Boundary Value Problems in Ordinary Differential Equations. Lecture Notes in Computer Science 76, Springer-Verlag.

    Google Scholar 

  3. U. Ascher, J. Christiansen and R.D. Russell, Collocation software for boundary value ODE's, 1980, ACMT, Math. 7, 209 (1981).

    MATH  Google Scholar 

  4. U. Ascher and R.D. Russell, Reformulation of boundary value problems into "standard" form, 1980, SIAM Rev. 23, 238 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  5. C. de Boor and B. Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Bulirsch, J. Stoer and P. Dauflhand, Numerical Solution of Nonlinear Two-Point Boundary Value Problems, 1980, Num. Math., Handbook Series Approximation, in preparation.

    Google Scholar 

  7. G.F. Carey and B.A. Finlayson, Orthogonal collocation on finite elements, Chem. Engr. Sci. 30 (1975), 587–596.

    Article  Google Scholar 

  8. J.H. Cerutti, Collocation for systems of ordinary differential equations, Comp. Sci. Tech. Rep. #230 (1974), University of Wisconsin, Madison.

    Google Scholar 

  9. E. Doedel, The numerical computation of branches of periodic solutions, 1980, submitted for publication.

    Google Scholar 

  10. B.A. Finlayson, The Method of Weighted Residuals and Variational Principles, Academic Press, N.Y., 1972.

    MATH  Google Scholar 

  11. G.E. Forsythe, M.A. Malcolm and C.B. Moler, Computer Methods for Mathematical Computations, 1977, Prentice-Hall, Englewood Cliffs, N.J.

    MATH  Google Scholar 

  12. I. Gladwell, A survey of subroutines for solving boundary value problems in ordinary differential equations, 1979, in Proc. of Conf. on Computational Techniques for ODEs, University of Manchester.

    Google Scholar 

  13. H.B. Keller and A.B. White, Jr., Difference methods for boundary-value problems in ordinary differential equations, SINUM 12 (1975), 791–801.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Lentini and V. Pereyra, An adaptive finite difference solver for non-linear two point boundary problems with mild boundary layers, SIAM J. Numer. Anal. 14 (1977), 91–111.

    Article  MathSciNet  MATH  Google Scholar 

  15. V. Pereyra and R.D. Russell, Manuscript in preparation, 1980.

    Google Scholar 

  16. R.D. Russell and L.F. Shampine, A collocation method for boundary value problems, Numer. Math. 19 (1972), 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  17. S.W. Schoombie and J.F. Botha, Error estimates for the solution of the radical Schrödinger equation by the Rayleigh-Ritz finite element method, 1980, to appear in J. Comp. Phys.

    Google Scholar 

  18. M.L. Scott and H.A. Watts, Computational solutions of linear two-point boundary value problems via orthonormalization, SIAM J. Numer. Anal. 14 (1977), 40–70.

    Article  MathSciNet  MATH  Google Scholar 

  19. A.B. White, Jr., On selection of equidistributing meshes for two-point boundary-value problems, SINUM 16 (1979), 472–502.

    Article  MathSciNet  MATH  Google Scholar 

  20. G.M. Vainniko, On convergence of the collocation method for nonlinear differential equations, USSR Comp. Math. & Math. Phys. 6 (1966), 35–42.

    Article  MathSciNet  Google Scholar 

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Juergen Hinze

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© 1982 Springer-Verlag

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Russell, R.D. (1982). Global codes for BVODEs and their comparison. In: Hinze, J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064893

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  • DOI: https://doi.org/10.1007/BFb0064893

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