Convergence Analysis of Sinc-Collocation Scheme With Composite Trigonometric Function for Fredholm Integral Equations of the Second Kind


  • Eno John Akwa Ibom State Polytechnic, Ikot Osurua
  • Promise Asukwo Federal Polytechnic, Ukana
  • Nkem Ogbonna Michael Okpara University of Agriculture, Umudike


Fredholm integral equations of the second kind, Composite trigonometric function, Sinc approximation, Collocation method, Convergence analysis


Communication in Physical Sciences, 2024, 11(3): 463-475

Authors: Eno John, Promise Asukwo and Nkem Ogbonna

Received: 24 January 2024/Accepted:06 June 2024

The paper discusses the convergence of Sinc collocation scheme for the solution of Fredholm integral equation of the second kind. A modified composite trigonometric function is employed as a variable transformation function for this procedure. We first show that the constructed variable transformation function decays exponentially and thus satisfies the conditions for the error bound associated with single exponential transformation functions. Next, the convergence analysis of the scheme showing exponential convergence is discussed. Finally, some numerical examples are presented to illustrate the efficiency and stability of the numerical scheme.


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Author Biographies

Eno John , Akwa Ibom State Polytechnic, Ikot Osurua

Department of General Studies

Promise Asukwo, Federal Polytechnic, Ukana

Department of Statistics

Nkem Ogbonna, Michael Okpara University of Agriculture, Umudike

Department of Mathematics


John, E, Promise, A. & Nkem. O. (2024). Solution of Fredholm integral equations of second kind using a composite trigonometric function, GPH International Journal of Mathematics, 7, 3, pp. 108 - 121.

John, E. D. (2016). Analysis of convergence of the solution of Volterra integral equations by Sinc collocation method, Journal of Chemical, Mechanical and Engineering Practice, International Perspective, 6, 1, 2, pp. 16 – 27.

Maleknejad, K., Mollopourasl, M. & Alizadeh, M. (2011). Convergence analysis numerical solution of Fredholm integral equation by Sinc approximations, Communications in Nonlinear Science and Numerical Simulation, 16, 6, pp. 2478-2485.

Muhammad, M. & Mori, M. (2003). Double exponential formulas for numerical indefinite integration, Journal of Computational and Applied Mathematics, 161, pp. 431-448.

Okayama, T. (2023). Sinc collocation method with constant collocation points for Fredholm integral equation of the second kind, Dolomite Research Notes on Approximation, 16(, 3, pp. 67 – 74. doi: 10.14658/PUPJ-DRNA-2023-3-9

Okayama, T., Matsuo, T. & Sugihara, M. (2011). Improvement of Sinc- collocation method for Fredholm integral equations of the second kind, BIT Numer. Math. 51, pp.339-366.

Stenger, F. (2011). Handbook of Sinc Numerical Methods. CRC Press.

Stenger, F. (1993). Numerical methods based on Sinc and analytic functions, Springer-Verlag, New York.

Sugihara, M. (2002). Near optimality of Sinc approximations. Mathematics of Computation, 72, 242, pp. 767-786.

Wazwaz, A. (2011). Linear and nonlinear integral equations, methods and applications, Higher education press, Beijing and Springer-Verlag Heidelberg.

Wei, J., & Yang, L. (2019). Numerical solution of integral equations using composite trigonometric functions. Journal of Computational and Applied Mathematics, 350,, pp. 12-123.

Zabihi, F. (2024). The use of Sinc-collocation method for solving steady–state concentrations of carbon‎ ‎dioxide absorbed into phenyl glycidyl ether. Computational Methods for Differential Equations, . doi: 10.22034/cmde.2024.55413.2304.

Zarebnia, M. and Rashidinia, J. (2010). Convergence of the Sinc method applied to Volterra integral equations, Applications and Applied Mathematics, 5, 1, pp. 198-216.

Zhang, X., Li, H., & Sun, J. (2022). Improved Sinc-collocation methods for integral equations with applications. Applied Numerical Mathematics, 175, pp. 233-247.