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Hybrid Functions of Lagrange Polynomials and Block-Pulse Functions for Solving Integro-partial Differential Equations

  • Nasibeh Mollahasani
  • Mahmoud Mohseni Moghadam
  • Gennady Chuev
Research Paper
  • 4 Downloads

Abstract

We construct two-dimensional hybrid functions from Lagrange polynomials and block-pulse functions. Using special properties of the functions for evaluating integral and derivatives, we develop an efficient algorithm for solving two-dimensional integro-differential equations. Some numerical examples are given to demonstrate the performance of the method.

Keywords

Hybrid methods Lagrange polynomials Block-pulse functions Integro-partial differential equations 

Mathematics Subject Classification

45-XX 45K05 34K10 

References

  1. Aghazadeh N, Khajehnasiri AA (2013) Solving nonlinear two-dimensional Volterra integro-differential equations by block-pulse functions. Math Sci 7:1–6MathSciNetCrossRefzbMATHGoogle Scholar
  2. Avudainayagam A, Vani C (2000) Wavelet Galerkin method for integro–differential equations. Appl Numer Math 32:247–254MathSciNetCrossRefzbMATHGoogle Scholar
  3. Canuto C, Hussaini MY, Quarteroni A, Zang TA (1988) Spectral methods in fluid dynamics. Springer, HeidelbergCrossRefzbMATHGoogle Scholar
  4. Hsiao Chun-Hui (2009) Hybrid function method for solving Fredholm and Volterra integral equations of the second kind. J Comput Appl Math 230:59–68MathSciNetCrossRefzbMATHGoogle Scholar
  5. Maleknejad K, Hashemizadeh E (2011) Numerical solution of the dynamic model of a chemical reactor by hybrid functions. Proc Comput Sci 3:908–912CrossRefGoogle Scholar
  6. Maleknejad K, Mahmoudi Y (2004) Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block-pulse-functions. Appl Math Comput 149:799–806MathSciNetzbMATHGoogle Scholar
  7. Maleknejad K, Tavassoli Kajani M (2004) Solving linear integro-differential equation system by Galerkin methods with hybrid functions. Appl Math Comput 159:603–612MathSciNetzbMATHGoogle Scholar
  8. Mashayekhi S, Ordokhani Y, Razzaghi M (2012) Hybrid functions approach for nonlinear constrained optimal control problems, commun. Nonlinear Sci Numer Simul 17:1831–1843MathSciNetCrossRefzbMATHGoogle Scholar
  9. Mohseni Moghadam M, Saeedi H (2010) Application of differential transforms for solving the Volterra integro-partial differential equations. Iran J Sci Technol 34:59–70MathSciNetGoogle Scholar
  10. Saeedi H (2013) Application of Haar wavelets in solving nonlinear fractional Fredholm integro-differential equations. J Mahani Math Res Cent 2:15–28Google Scholar
  11. Saeedi H, Mohseni Moghadam M, Mollahasani N, Chuev G (2011) A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order. Commun Nonlinear Sci Numer Simul 16:1154–1163MathSciNetCrossRefzbMATHGoogle Scholar
  12. Zhao J, Corless RM (2006) Compact finite difference method for integro-differential equations. Appl Math Comput 177:271–288MathSciNetzbMATHGoogle Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Nasibeh Mollahasani
    • 1
  • Mahmoud Mohseni Moghadam
    • 1
  • Gennady Chuev
    • 2
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and ComputerShahid Bahonar University of KermanKermanIran
  2. 2.Institute of Theoretical and Experimental BiophysicsMoscowRussia

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