Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 11 2 2024 10 01 Using of rational Haar wavelet to solve of nonlinear integro-differential equations حل معادلات اینتگرو دیفرانسیل فردهلم با کمک موجک هار 66 75 718039 10.22072/wala.2024.2031651.1454 EN Majid Erfanian Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran 0000-0001-8449-9272 Hamed Zeidabadi Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran Journal Article 2024 06 09 This article uses the rational Haar wavelet and the successive method<br />to solve the nonlinear Fredholm integral differential equation. Additionally, we<br />have proved the convergence and order of convergence in this method by using<br />the fixed point Banach theorem. In this way, numerical integration is not used.<br />We also talk about two examples. We solved, drawing the absolute error, and<br />plot of the exact and numerical solution. Finally, the results show that the<br />proposed method is powerful for solving this equation. nonlinear Fredholm integral differential equation Convergence fixed point Banach theorem Haar Wavelet absolute error https://wala.vru.ac.ir/article_718039_586f2a54b48efc55a511efb8f9be2043.pdf