MMN-2930

A numerical method for a second order singularly perturbed Fredholm integro-differential equation

  • Gabil M. Amiraliyev, Erzincan Binali Yildirim University, Faculty of Arts and Sciences, Department of Mathematics, 24100 Erzincan, Turkey, gabilamirali@yahoo.com
  • Muhammet Enes Durmaz, Kirklareli University, Department of Information Technology, 39000 Kirklareli, Turkey, menesdurmaz025@gmail.com
  • Mustafa Kudu, Erzincan Binali Yildirim University, Faculty of Arts and Sciences, Department of Mathematics, 24100 Erzincan, Turkey, muskud28@yahoo.com

Abstract

The boundary-value problem for a second order singularly perturbed Fredholm integro-differential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fi tted difference scheme on an uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic.


Vol. 22 (2021), No. 1, pp. 37-48
DOI: 10.18514/MMN.2021.2930


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