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The numerical solution of differential-algebraic equations by sinc-collocation method

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Abstract

In this article, numerical solution of differential-algebraic equations (DAEs), by means of the sinc-collocation method is considered. Properties of the sinc procedure are utilized to reduce the computation of the DAEs to systems of algebraic equations. It is well known that the sinc procedure converges to the solution at an exponential rate. To show the validity and efficiency of the present method, some examples are presented. The method is easy to implement and the results show that this method is very efficient, and can be applied to a large class of problems.

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References

  • Ascher UM, Lin P (1996) Sequential regularization methods for higher index differential-algebraic equations with constraint singularities: the linear index-2 case. SIAM J Numer Anal 33:1921–1940

    Article  MathSciNet  MATH  Google Scholar 

  • Ascher UM, Petzold LR (1991) Projected implicit Runge-Kutta methods for differential-algebraic equations. SIAM J Numer Anal 28:1097–1120

    Article  MathSciNet  MATH  Google Scholar 

  • Ascher UM, Petzold LR (1993) Stability of computational methods for constrained dynamical systems. SIAM J Sci Comput 14:95–120

    Article  MathSciNet  MATH  Google Scholar 

  • Babolian E, Hosseini MM (2003) Reducing index, and pseudospectral methods for differential-algebraic equations. Appl Math Comput 140:77–90

    Article  MathSciNet  MATH  Google Scholar 

  • Brenan KE, Campbell SL, Petzold LR (1989) Numerical solution of initial-value problems in differential algebraic equations. Elsevier, New York

    MATH  Google Scholar 

  • Dehghan M, Saadatmandi A (2007) The numerical solution of a nonlinear system of second-order boundary value problems using Sinc-collocation method. Math Comput Model 46:1434–1441

    Article  MathSciNet  MATH  Google Scholar 

  • Gear CW, Petzold LR (1984) ODE methods for the solution of differential-algebraic systems. SIAM J Numer Anal 21:716–728

    Article  MathSciNet  MATH  Google Scholar 

  • Hosseini MM (2005) An index reduction method for linear Hessenberg systems. J Comput Appl Math 171:596–603

    Article  MathSciNet  MATH  Google Scholar 

  • Hosseini MM (2006) Adomian decomposition method for solution of differential algebraic equations. J Comput Appl Math 197:495–501

    Article  MathSciNet  MATH  Google Scholar 

  • Koonprasert S, Bowers KL (2004) Block matrix sinc-galerkin solution of the wind-driven current problem. Appl Math Comput 155:607–635

    Article  MathSciNet  MATH  Google Scholar 

  • Lund J, Bowers KL (1992) Sinc methods for quadrature and differential equations. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Mohsen A, El-Gamel M (2010) On the numerical solution of linear and nonlinear volterra integral and integro-differential equations. Appl Math Comput 217:3330–3337

    Article  MathSciNet  MATH  Google Scholar 

  • Parand K, Dehghan M, Pirkhedri A (2009) Sinc-collocation method for solving the Blasius equation. Phys Lett A 373:4060–4065

    Article  MathSciNet  MATH  Google Scholar 

  • Revelli R, Ridolfi L (2003) Sinc collocation-interpolation method for the simulation of nonlinear waves. Comput Appl Math. 46:1443–1453

    MathSciNet  MATH  Google Scholar 

  • Saadatmandi A (2012) Numerical study of Second Painlevé equation. Commun Numer Anal 2012. Article ID cna-00157, 16 pages.

  • Saadatmandi A, Dehghan M (2012) The use of Sinc-collocation method for solving multi-point boundary value problems. Commun Nonlinear Sci Numer Simulat 17:593–601

    Article  MathSciNet  MATH  Google Scholar 

  • Saadatmandi A, Dehghan M, Azizi MR (2012) The Sinc-Legendre collocation method for a class of fractional convection-diffusion equations. Commun Nonlinear Sci Numer Simulat 17:4125–4136

    Article  MathSciNet  MATH  Google Scholar 

  • Saadatmandi A, Razzaghi M, Dehghan M (2005) Sinc-collocation methods for the solution of Hallen’s integral equation. J Electromagn Wave Appl 19:245–256

    Article  MathSciNet  Google Scholar 

  • Saadatmandi A, Razzaghi M, Dehghan M (2005) Sinc-galerkin solution for nonlinear two-point boundary value problems with applications to chemical reactor theory. Math Comput Model 42:1237–1244

    Article  MathSciNet  MATH  Google Scholar 

  • Saadatmandi A, Razzaghi M (2007) The numerical solution of third-order boundary value problems using Sinc-collocation method. Commun numer method eng 23:681–689

    Article  MathSciNet  MATH  Google Scholar 

  • Soltanian F, Dehghan M, Karbassi SM (2010) Solution of the differential-algebraic equations via homotopy perturbation method and their engineering applications. Int J Comput Math 87:1950–1974

    Article  MathSciNet  MATH  Google Scholar 

  • Soltanian F, Karbassi SM, Hosseini MM (2009) Application of He’s variational iteration method for solution of differential-algebraic equations. Chaos Soliton Fract 41:436–445

    Article  MATH  Google Scholar 

  • Stenger F (1993) Numerical methods based on sinc and analytic functions. Springer, New York

    Book  MATH  Google Scholar 

  • Stenger F, Cook T, Kirby RM (2004) Sinc solution of biharmonic problems. Canad Appl Math Q 12:371–414

    MathSciNet  Google Scholar 

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Acknowledgments

A. Saadatmandi would like to acknowledge the University of Kashan for support of this research by a grant (No. 159026).

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Authors and Affiliations

  1. Department of Mathematics, Natanz Branch, Islamic Azad University, Natanz, Islamic Republic of Iran

    Somayeh Yeganeh

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 87317-51167, Islamic Republic of Iran

    Abbas Saadatmandi

  3. Department of Mathematics, Payame Noor University, PO Box 19395-3697, Tehran, Islamic Republic of Iran

    Fahimeh Soltanian

  4. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No.424, Hafez Ave, Tehran, Islamic Republic of Iran

    Mehdi Dehghan

Authors
  1. Somayeh Yeganeh
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  2. Abbas Saadatmandi
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  3. Fahimeh Soltanian
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  4. Mehdi Dehghan
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Corresponding author

Correspondence to Abbas Saadatmandi.

Additional information

Communicated by Antonio Silva Neto.

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Yeganeh, S., Saadatmandi, A., Soltanian, F. et al. The numerical solution of differential-algebraic equations by sinc-collocation method. Comp. Appl. Math. 32, 343–354 (2013). https://doi.org/10.1007/s40314-013-0024-8

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  • DOI: https://doi.org/10.1007/s40314-013-0024-8

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