Haar Wavelets and Multiple-Scale Pascal Polynomial Triangle Methods for Solving Nonlinear Volterra Integral Equations

Kurda   Hussein; Mudhafar  F. Hama

doi:10.25098/6.2.30

Authors

Kurda Hussein Mathematics Department, College of Education, University of Sulaimani, Sulaimaniya, Iraq
Mudhafar F. Hama Mathematics Department, College of Science, University of Sulaimani, Sulaimaniya, Iraq

DOI:

https://doi.org/10.25098/6.2.30

Keywords:

Nonlinear, Volterra integral equations, Haar wavelets method, multiple-scale method, Pascal polynomial 2020 MSC: 45G10, 45D05, 65T60, 34E13, 65R20, 65D15

Abstract

The aim of this paper is to propose a numerical approximation method to solve nonlinear Volterra integral equations of the second kind using Haar wavelets and multiple-scale Pascal polynomial methods. These methods are specifically derived for nonlinear problems. In this numerical approximation, we do not need to use numerical integration which is one of the advantages of our proposed method. Numerical examples are tested to demonstrate the validity of the method and the efficiency of the method is confirmed.

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