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Sinc Collocation Solutions for the Integral Algebraic Equation of Index-1

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  08 July 2016

Jingjun Zhao ,
Yang Cao  and
Yang Xu
Jingjun Zhao*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Yang Cao
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Yang Xu*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
*
*Corresponding author. Email:hit_zjj@hit.edu.cn (J. J. Zhao), yangx@hit.edu.cn (Y. Xu)
*Corresponding author. Email:hit_zjj@hit.edu.cn (J. J. Zhao), yangx@hit.edu.cn (Y. Xu)
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Abstract

In this article, Sinc collocation method is considered to obtain the numerical solution of integral algebraic equation of index-1 by reducing it to an explicit system of algebraic equation. It is shown that Sinc collocation solution can produce an error of order . Moreover, Sinc method is applied to several examples to illustrate the accuracy and implementation of the method.

Keywords

Integral algebraic equation of index-1Sinc methodexponential convergence

MSC classification

Secondary: 65L20: Stability and convergence of numerical methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 757 - 771
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Al-Khaled, K., Numerical approximations for population growthmodels, Appl. Math. Comput., 160 (2005), pp. 865–873.Google Scholar
[2]Brunner, H., Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge University Press, Cambridge, 2004.CrossRefGoogle Scholar
[3]Cannon, J. R., The One Dimensional Heat Equation, Cambridge University Press, Cambridge, 1984.CrossRefGoogle Scholar
[4]Gear, C. W., Differential-algebraic equations, indices, and integral-algebraic equations, SIAM Numer. Anal., 27 (1990), pp. 1527–1534.CrossRefGoogle Scholar
[5]Gomilko, A. M., A Dirichlet problem for the biharmonic equation in a semi-infinite strip, J. Eng. Math., 46 (2003), pp. 253–268.CrossRefGoogle Scholar
[6]Hadizadeh, M., Ghoreishi, F. and Pishbin, S., Jacobi spectral solution for integral-algebraic equations of index-2, Appl. Numer. Math., 61 (2011), pp. 131–148.CrossRefGoogle Scholar
[7]Kafarov, V. V., Mayorga, B. and Dallos, C., Mathematical method for analysis of dynamic processes in chemical reactors, Chem. Eng. Sci., 54 (1999), pp. 4669–4678.CrossRefGoogle Scholar
[8]Kauthen, J. P., The numerical soluton of integral-algebraic equations of index-1 by polynomial spline collocation methods, Math. Comput., 236 (2000), pp. 1503–1514.CrossRefGoogle Scholar
[9]Pishbin, S., Ghoreishi, F. and Hadizadeh, M., A posteriori error estimation for the Legendre collocation method applied to integral-algebraic Volterra equations, Electron. Trans. Numer. Anal., 38 (2011), pp. 327–346.Google Scholar
[10]Rashidinia, J. and Zarebnia, M., Solution of a Volterra integral equation by the Sinc-collocation method, J. Comput. Appl. Math., 206 (2007), pp. 801–813.CrossRefGoogle Scholar
[11]Smith, R. C., Bogar, G. A., Bowers, K. L. and Lund, J., The Sinc-Galerkin method for fourth-order differential equations, SIAM J. Numer. Anal., 28 (1991), pp. 760–788.CrossRefGoogle Scholar
[12]Smith, R. C., Bowers, K. L. and Lund, J., Fully Sinc-Galerkin method for Euler-Bernoulli beam modles, Numer. Methods Partial Differential Equations, 8 (1992), pp. 171–202.CrossRefGoogle Scholar
[13]Smith, R. C. and Bowers, K. L., A Sinc-Galerkin estimation of diffusivity in parabolic problems, Inverse. Probl., 9 (1993), pp. 113–145.CrossRefGoogle Scholar
[14]Stenger, F., Numerical Methods Based on Sinc and Analytic Functions, Springer-Verlag, New York, 1993.CrossRefGoogle Scholar
[15]Sugihara, M. and Matsuo, T., Recent developments of the Sinc numerical methods, J. Comput. Appl. Math., 164-165 (2004), pp. 673–689.CrossRefGoogle Scholar
[16]Winnter, D. F., Bowers, K. L. and Lund, J., Wind-driven currents in a sea with variable eddy viscosity calculated via a Sinc-Galerkin technique, J. Numer. Methods Fluids, 33 (2000), pp. 1041–1073.3.0.CO;2-P>CrossRefGoogle Scholar
[17]Zarebnia, M., Sinc numerical solution for the Volterra integro-differential equation, Commun. Nonlinear Sci. Numer. Simulat., 15 (2010), pp. 700–706.CrossRefGoogle Scholar