A New Iterative Method of Successive Approximation to Solve Nonlinear Urysohn Integral Equations by Haar Wavelet

Subject Areas : International Journal of Mathematical Modelling & Computations

Manochehr  Kazemi ¹ (Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran)
Vali  Torkashvand ² (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran)
Einollah  Fathizade ³ (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran)

Received: 2020-07-14 Accepted : 2020-10-16 Published : 2020-12-01

Keywords: Haar wavelet, Lipschitz condition, Integral equations, Successive approximations,

Abstract :

In this paper, a new method for calculating the numerical approximation of the nonlinear Urysohn integral equations is proposed based on Haar wavelets. Also, the convergence analysis and numerical stability of these method are discussed. Conducting numerical experiments confirm the theoretical results of the applied method and endorse the accuracy of the method.