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Solving Integral equations on Semi-Infinite Intervals via Rational third kind Chebyshev functions

Author Affiliations

  • 1Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, IRAN
  • 2 Department of Mathematics, Faculty of Sciences, University of Isfahan, Isfahan, IRAN
  • 3 Department of Mathematics, Khorasgan Branch, Islamic Azad University, Isfahan, IRAN

Res. J. Recent Sci., Volume 3, Issue (12), Pages 75-77, December,2 (2014)

Abstract

In this paper, we employ the rational third kind Chebyshev functions on the interval (0, ∞) to solve the linear integral equations of the second kind over infinite intervals. The properties of the rational third kind Chebyshev functions together with the Galerkin method are applied to reduce the integral equation to a system of linear algebraic equations. Using two numerical examples, we show that our estimates have a good degree of accuracy.

References

  1. Maleknejad K. and Yousefi M., Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines, Applied Mathematics and Computation, 183(1) 134-141 (2006)
  2. Mahmoudi Y., Wavelet Galerkin method for numerical solution of nonlinear integral equation, Applied Mathematics and Computation, 167(2) 1119-1129 (2005)
  3. Maleknejad K., Tavassoli Kajani M. and Mahmoudi Y., Numerical solution of linear Fredholm and volterra integral equation of the second kind by using Legendre wavelets, Kybernetes 32(9/10) 1530-1539 (2003)
  4. Gu C. and Shen J., Function-valued Padé-type approximant via the formal orthogonal polynomials and its applications in solving integral equations, Journal of Computational and Applied Mathematics, 221(1) 114-131 (2008)
  5. Abdou M.A., Integral equation of mixed type and integrals of orthogonal polynomials, Journal of Computational and Applied Mathematics, 138(2) 273-285 (2002)
  6. Asady B., Tavassoli Kajani M., Hadi Vencheh A. and Heydari A., Solving second kind integral equations with hybrid Fourier and block–pulse functions, Applied Mathematics and Computation, 160(2) 517-522 (2005)
  7. Tavassoli Kajani M. and Hadi Vencheh A., Solving second kind integral equations with Hybrid Chebyshev and Block-Pulse functions, Applied Mathematics and Computation, 163(1) 71-77 (2005)
  8. Vahdati S., Tavassoli Kajani M. and Ghasemi M., Application of Homotopy Analysis Method to SIR Epidemic Model, Reseaech Journal of Recent Sciences, 2(1) 91-96 (2013)
  9. Muhammad Altaf Khan, et al, Application of Homotopy Perturbation Method to Vector Host Epidemic Model with Non-Linear Incidences, Reseaech Journal of Recent Sciences, 2(6) 90-95 (2013)
  10. Abramowitz M. and Stegun I.A., Handbook of Mathematical Functions, 10th printing with corrections, Dover, New York, 1972.
  11. Tavassoli Kajani M. and Ghasemi Tabatabaei F., Rational Chebyshev approximations for solving Lane-Emde equation of index m, in : Proceeding of the International Conference on Computational and Applied Mathematics, Bangkok, Thailand March 29-31, 840-844 (2011)
  12. Dadkhah Tirani M., Ghasemi Tabatabaei F. and Tavassoli Kajani M., Rational second (third) kind Chebyshev approximations for solving Volterra’s population model, in : Proceeding of the International Conference on Computational and Applied Mathematics, Bangkok, Thailand March, 29-31, 835-839 (2011)