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Haar Wavelet Method for the Numerical Solution of Nonlinear Fredholm Integro-Differential Equations | ||
| Journal of Education and Science | ||
| Article 2, Volume 32, Issue 4, December 2023, Pages 10-25 PDF (865.88 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/edusj.2023.139892.1360 | ||
| Authors | ||
| Najem A. Mohammad1; Younis Sabawi* 2; Mohammad Shami Hasso3 | ||
| 11Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOYA45, Kurdistan Region-F.R. Iraq. | ||
| 2Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Kurdistan Region - F.R. Iraq | ||
| 3Department of Mathematics - Koya University | ||
| Abstract | ||
| The solution of nonlinear Fredholm integro-differential equations plays a significant role in analyzing many nonlinear events that occur in chemistry, physics, mathematical biology, and a variety of other fields of science and engineering. A physical event can be represented by a differential equation, an integro-differential equation since many of these equations cannot be solved directly or it is difficult to solve. Numerical approaches that are useful combinations of numerical integration must frequently be used. This work presents a method for solving the type of nonlinear Fredholm integro-differential equation (NFIDE) of the second kind. The Leibnitz rule is used with the Haar wavelet collocation method in this paper to solve NFIDE numerically. Some techniques are used to transfer the equation into an algebraic system through an operational matrix. The convergence analysis had been proved through this work and the numerical experiments had been given to illustrate the effectiveness of the proposed method based on MATLAB programming. | ||
| Keywords | ||
| Second order Nonlinear integro-differential equations,,; ,،numerical solution,,; ,،Haar wavelet,,; ,،Leibnitz rule,,; ,،Convergence Analysis of Haar wavelet method | ||
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