Hermite bicubic spline collocation method for Poisson's equations

Authors

  • Mihaela Puşcaş Fundatia Universitara AISTEDA, Alba-Iulia, Romania

DOI:

https://doi.org/10.33993/jnaat331-763

Keywords:

spline approximating solution, Dirichlet problem, Poisson's equation, smooth approximation, bicubic spline collocation
Abstract views: 210

Abstract

In this paper is presented a bicubic spline collocation method for the numerical approximation of the solution of Dirichlet problem for the Poisson's equation. The approximating solution is effectively determined in a bicubic Hermite spline functions space by using a suitable basis constructed as a tensorial product of univariate spline spaces.

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References

Bialecki, B. and Cai, X. C., H¹-norm error bounds for piecewise Hermite bicubic orthogonal spline collocation method for elliptic boundary value problems, SIAM J. Numer. Anal., 31, pp. 1128-1146, 1994, https://doi.org/10.1137/0731059 DOI: https://doi.org/10.1137/0731059

Bialecki, B., Fairweather, G. and Bennett, K. R., Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations, SIAM J. Numer. Anal., 29, pp. 156-173, 1992, https://doi.org/10.1137/0729010 DOI: https://doi.org/10.1137/0729010

Ciarlet, P. G., The finite element method for elliptic problems, North Holland Publ. Comp., Amsterdam, 1978, https://doi.org/10.1137/1.9780898719208 DOI: https://doi.org/10.1137/1.9780898719208

Ciarlet, P. G. and Glowinski, R., Dual iterative techniques for solving a finite element approximation for the biharmonic equation, Comp. Maths. Appl. Mech. Eng., 5, pp. 277-295, 1975, https://doi.org/10.1016/0045-7825(75)90002-x DOI: https://doi.org/10.1016/0045-7825(75)90002-X

Dillery, D. S., High order orthogonal spline collocation schemes for elliptic and parabolic problems, Ph. D. Thesis, Univerity of Kentucky, Lexington, 1994.

Douglas, J. and Dupont, T., Collocation methods for parabolic equations in a single space variable, Lect. Notes in Maths., Springer-Verlag, 1974, https://doi.org/10.1007/bfb0057337 DOI: https://doi.org/10.1007/BFb0057337

Hackbusch, W., Elliptic differential equations. Theory and numerical treatments, Springer-Verlag, 1992, https://doi.org/10.1007/978-3-642-11490-8 DOI: https://doi.org/10.1007/978-3-642-11490-8_10

Hollig, K., Reif, U. and Wipper, J., Wieghted extended B-spline approximation of Dirichlet problems, SIAM J. Numer. Anal., 39, pp. 442-462, 2001,https://doi.org/10.1137/s0036142900373208 DOI: https://doi.org/10.1137/S0036142900373208

Houstis, E. N., Vavalis, E. A. and Rice, J. R., Convergence of O(h⁴) cubic spline collocation methods for elliptic partial differential equations, SIAM J. Numer. Anal., 25, pp. 54-74, 1988, https://doi.org/10.1137/0725006 DOI: https://doi.org/10.1137/0725006

Micula, G., Funcţii spline şi aplicaţii, Editura Tehnică, Bucureşti, 1978.

Micula, G. and Micula, S., Handbook of splines, Kluwer Acad. Publ. Boston-London, 1999, https://doi.org/10.1007/978-94-011-5338-6_10 DOI: https://doi.org/10.1007/978-94-011-5338-6

Percell, P. and Wheeler, M. F., A C1 finite collocation method for elliptic equations, SIAM J. Numer. Anal., 17, pp. 605-622, 1980, https://doi.org/10.1137/0717050 DOI: https://doi.org/10.1137/0717050

Prenter, P. M. and Russel, R. D., Orthogonal collocation for elliptic partial differential equations, SIAM J. Numer. Anal., 13, pp. 923-939, 1976, https://doi.org/10.1137/0713073 DOI: https://doi.org/10.1137/0713073

Zhuo-Ming Lou, Orthogonal spline collocation for biharmonic problems, Ph. D. Thesis, University of Kentucky, Lexington, 1996.

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Published

2004-02-01

How to Cite

Puşcaş, M. (2004). Hermite bicubic spline collocation method for Poisson’s equations. Rev. Anal. Numér. Théor. Approx., 33(1), 87–94. https://doi.org/10.33993/jnaat331-763

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