Browsing by Author "Amin, Rohul"

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Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method
(2020) Abdeljawad, Thabet; Jarad, Fahd; Shah, Kamal; Al-Mdallal, Qasem; Jarad, Fahd; 234808
This manuscript deals a numerical technique based on Haar wavelet collocation which is developed for the approximate solution of some systems of linear and nonlinear fractional order differential equations (FODEs). Based on these techniques, we find the numerical solution to var-ious systems of FODEs. We compare the obtain solution with the exact solution of the considered problems at integer orders. Also, we compute the maximum absolute error to demonstrate the effi-ciency and accuracy of the proposed method. For the illustration of our results we provide four test examples. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is defined in the Caputo sense. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
On a new method for finding numerical solutions to integro-differential equations based on Legendre multi-wavelets collocation
(2022) Jarad, Fahd; Asif, Muhammad; Amin, Rohul; Al-Mdallal, Qasem; Jarad, Fahd; 234808
In this article, a wavelet collocation method based on linear Legendre multi-wavelets is proposed for the numerical solution of the first as well as higher orders Fredholm, Volterra and Volterra–Fredholm integro-differential equations. The presented numerical method has the capability to tackle the solutions of both linear and nonlinear problems of these model equations. In order to endorse accuracy and efficiency of the method, it is tested on various numerical problems from literature with the aid of maximum absolute errors and rates of convergence. L∞ norms are used to compare the numerical results with other available methods such as Multi-Scale-Galerkin's method, Haar wavelet collocation method and Meshless method from literature. The comparability of the presented method with other existing numerical methods demonstrates superior efficiency and accuracy.