Hermite bicubic spline collocation method for Poisson's equations


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




spline approximating solution, Dirichlet problem, Poisson's equation, smooth approximation, bicubic spline collocation
Abstract views: 184


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.


Download data is not yet available.


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.




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