Galerkin approximation for a semi linear parabolic problem with nonlocal boundary conditions
DOI:
https://doi.org/10.4067/S0716-09172004000100003Keywords:
Semi-linear parabolic problem, nonlocal boundary conditions, θ-Galerkin method, problema parabólico semilineal, condiciones de acotamiento no-local, método θ-Galerkin.Abstract
We analyze a ?-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 ? ? 1/2, numerical application is given.References
[1] A. Boutayeb, A. Chetouani, Global extrapolations of numerical methods for a parabolic problem with nonlocal boundary conditions, International journal of computer mathematics 80, No. 6, pp. 789-797, (2003).
[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, (1982).
[3] W. A. Day, A decreasing property of solutions of parabolic equations with apllications to thermoelasticity, Quart. Appl. Math. 40, pp. 468-475, (1983).
[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 Computational mathematics 6, pp. 243-262, (1996).
[6] A. Friedman, Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions, Quart. Appl. Math. 44, pp. 401-407, (1986).
[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- 752, (1987).
[8] J. C. López-Marcos, J. M.Sanz-Serna, Stability and convergence in numerical analysis III: Linear investigation of nonlinear stability, IMAJ. Numer. Anal. 8, pp. 71-84, (1988)
[9] M. F. Wheeler, An optimal L? error estimate for Galerkin approximation to solutions of two boudary value problems, SIAMJ. Numer. Anal 10, pp. 914-917, (1973).
[10] J. C. López-Marcos, J. M.Sanz-Serna, A definition of stability for nonlinear problems, in: Numerical Treatment of Differential Equations, ed. K. Strehmel, Teubner Texte zur Mathematic (Teubner, Leipzig, pp. 216-226, (1988).
[11] G. Fairweather, J.C. López-Marcos, A.Boutayeb, Orthogonal Spline Collocation for a Quasilinear parabolic problem with nonlocal boundary conditions, Preprint.
[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, (1982).
[3] W. A. Day, A decreasing property of solutions of parabolic equations with apllications to thermoelasticity, Quart. Appl. Math. 40, pp. 468-475, (1983).
[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 Computational mathematics 6, pp. 243-262, (1996).
[6] A. Friedman, Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions, Quart. Appl. Math. 44, pp. 401-407, (1986).
[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- 752, (1987).
[8] J. C. López-Marcos, J. M.Sanz-Serna, Stability and convergence in numerical analysis III: Linear investigation of nonlinear stability, IMAJ. Numer. Anal. 8, pp. 71-84, (1988)
[9] M. F. Wheeler, An optimal L? error estimate for Galerkin approximation to solutions of two boudary value problems, SIAMJ. Numer. Anal 10, pp. 914-917, (1973).
[10] J. C. López-Marcos, J. M.Sanz-Serna, A definition of stability for nonlinear problems, in: Numerical Treatment of Differential Equations, ed. K. Strehmel, Teubner Texte zur Mathematic (Teubner, Leipzig, pp. 216-226, (1988).
[11] G. Fairweather, J.C. López-Marcos, A.Boutayeb, Orthogonal Spline Collocation for a Quasilinear parabolic problem with nonlocal boundary conditions, Preprint.
Published
2017-05-22
How to Cite
[1]
A. Boutayeb and A. Chetouani, “Galerkin approximation for a semi linear parabolic problem with nonlocal boundary conditions”, Proyecciones (Antofagasta, On line), vol. 23, no. 1, pp. 31-49, May 2017.
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