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Sinc-Galerkin solution for nonlinear two-point boundary value problems with applications to chemical reactor theory. (English) Zbl 1085.65065

Summary: The Sinc-Galerkin method is presented for solving nonlinear two-point boundary value problems for second order differential equations. A problem arising from chemical reactor theory is then considered. Properties of the Sinc-Galerkin method are utilized to reduce the computation of nonlinear two-point boundary value problems to some algebraic equations. The method is computationally attractive and applications are demonstrated through an illustrative example.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
80A32 Chemically reacting flows
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[1] Madbouly, N. M.; McGhee, D. F.; Roach, G. F., Adomian’s method for Hammerstein integral equations arising from chemical reactor theory, Applied Mathematics and Computation, 117, 249-341 (2001) · Zbl 1023.65143
[2] Poore, A., A tubular chemical reactor model, (A Collection of Nonlinear Model Problems Contributed to the Proceeding of the AMS-SIAM (1989)), 28-31
[3] Heinemann, R.; Poore, A., Multiplicity stability and oscillatory dynamics of the tubular reactor, Chemical Engineering Science, 36, 1411-1419 (1981)
[4] Heinemann, R.; Poore, A., The effect of activiation energy on tubular reactor multiplicity, Chemical Engineering Science, 37, 128-131 (1982)
[5] Stenger, F., Numerical Methods Based on Sinc and Analytic Functions (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0803.65141
[6] Lund, J.; Bowers, K., Sinc Methods for Quadrature and Differential Equations (1992), SIAM: SIAM New York · Zbl 0753.65081
[7] Lund, J.; Vogel., C., A Fully-Galerkin method for the solution of an inverse problem in a parabolic partial differential equation. numerical solution of an inverse, Inverse Problems, 6, 205-217 (1990) · Zbl 0709.65104
[8] Smith, R.; Bowers, K., A Sinc-Galerkin estimation of diffusivity in parabolic problems, Inverse Problems, 9, 113-135 (1993) · Zbl 0767.65093
[9] Bialecki, B., Sinc-collocation methods for two-point boundary value problems, IMA J. Numer. Anal, 11, 357-375 (1991) · Zbl 0735.65052
[10] Winter, D. F.; Bowers, K.; Lund, J., Wind-driven currents in a sea with a variable Eddy viscosity calculated via a Sinc-Galerkin technique, Internt. J. Numer. Methods Fluids, 33, 1041-1073 (2000) · Zbl 0984.76066
[11] Sababheh, M. S.; Al-khaled, A. M.N., Some convergence results on Sinc interpolation, J. Inequal. Pure and Appl. Math, 4, 32-48 (2003) · Zbl 1069.41005
[12] Mueller, J. L.; Shores, T. S., A new Sinc-Galerkin method for convection-diffusion equations with mixed boundary conditions, Computers Math. Applic., 47, 4/5, 803-822 (2004) · Zbl 1058.65083
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