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 , Vali Torkashvand ² , Einollah Fathizade ³

1 - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
2 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
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.