Wavelet and Linear Algebra

Using of rational Haar wavelet to solve of nonlinear integro-differential equations

Document Type : Research Paper

Authors

Majid Erfanian 1
Hamed Zeidabadi 2

1 Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran

2 Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran

10.22072/wala.2024.2031651.1454
Abstract
This article uses the rational Haar wavelet and the successive method
to solve the nonlinear Fredholm integral differential equation. Additionally, we
have proved the convergence and order of convergence in this method by using
the fixed point Banach theorem. In this way, numerical integration is not used.
We also talk about two examples. We solved, drawing the absolute error, and
plot of the exact and numerical solution. Finally, the results show that the
proposed method is powerful for solving this equation.

Keywords

nonlinear Fredholm integral differential equation
Convergence
fixed point Banach theorem
Haar Wavelet
absolute error
Wavelet and Linear Algebra
Volume 11, Issue 2
October 2024
Pages 66-75

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