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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.

65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B15Nonlinear boundary value problems for ODE
80A32Chemically reacting flows (thermodynamic aspects)
Full Text: DOI
[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, 28-31 (1989)
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[4] Heinemann, R.; Poore, A.: The effect of activiation energy on tubular reactor multiplicity. Chemical engineering science 37, 128-131 (1982)
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[6] Lund, J.; Bowers, K.: Sinc methods for quadrature and differential equations. (1992) · Zbl 0753.65081
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[8] Smith, R.; Bowers, K.: A sinc-Galerkin estimation of diffusivity in parabolic problems. Inverse problems 9, 113-135 (1993) · Zbl 0767.65093
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[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, No. 4/5, 803-822 (2004) · Zbl 1058.65083