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Galerkin approximation for a semi linear parabolic problem with nonlocal boundary conditions

  • Boutayeb, Abdesslam [1] ; Chetouani, Abdelaziz [1]
    1. [1] Université Mohammed I.
  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 23, Nº. 1, 2004, págs. 31-49
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172004000100003
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  • Resumen
    • We analyze a θ-method for the numerical solution of a semi linear parabolic problem with boundary conditions containing integrals over the interior of the interval. Existence and convergence are proved for θ ≥ 1/2, numerical application is given.

  • Referencias bibliográficas
    • Citas [1] A. Boutayeb, A. Chetouani, Global extrapolations of numerical methods for a parabolic problem with nonlocal boundary conditions,...
    • [2] W. A. Day, Extension of a property of the heat equation to linear thermoelasticity and other theories, Quart. Appl. Math. 40, pp. 319-330,...
    • [3] W. A. Day, A decreasing property of solutions of parabolic equations with apllications to thermoelasticity, Quart. Appl. Math. 40, pp....
    • [4] G. Ekolin, Finite difference methods for a nonlocal boundary value problem for the heat equation, BIT 31, pp. 245-261, (1991).
    • [5] G. Fairweather, J.C. López-Marcos, Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions, Advances in...
    • [6] A. Friedman, Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions, Quart. Appl. Math. 44, pp. 401-407,...
    • [7] A. Kawohl, Remarks on a paper by W. A. Day on a maximun principle under nonlocal boundary conditions, Quart. Appl. Math. 44, pp. 751-...
    • [8] J. C. López-Marcos, J. M.Sanz-Serna, Stability and convergence in numerical analysis III: Linear investigation of nonlinear stability,...
    • [9] M. F. Wheeler, An optimal L∞ error estimate for Galerkin approximation to solutions of two boudary value problems, SIAMJ. Numer. Anal...
    • [10] J. C. López-Marcos, J. M.Sanz-Serna, A definition of stability for nonlinear problems, in: Numerical Treatment of Differential Equations,...
    • [11] G. Fairweather, J.C. López-Marcos, A.Boutayeb, Orthogonal Spline Collocation for a Quasilinear parabolic problem with nonlocal boundary...

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