منصة إيفاد العلمية

مونيكا بطرس وديع

إرسال رسالة

التخصص: Mathematics

الجامعة: Delta University

النقاط:

12.5

معامل الإنتاج البحثي

الخبرات العلمية

اقوم بتدريس الرياضيات في كليات مختلفة: الهندسة و الذكاء الاصطناعي
اقوم ب اعمال الكنترول و الجودة

الأبحاث المنشورة

A continuous solution of solving a class of nonlineartwo point boundary value problem using Adomian decomposition method

المجلة: Ain Shams Engineering Journal

سنة النشر: 2019

تاريخ النشر: 2019-03-01

In this paper, a modified version of Adomian decomposition method is used to solve a class of nonlinear boundary value problems. It is easy to solve IVP using ADM but there exist some difficulties in solving BVP. But by using our modification of ADM, we solve the BVP by easily and directly method. As well we get a continuous solution of BVP. This technique gives a continuous solution and improves the work done by El-Kalla 2013. Some numerical examples are introduced to verify the efficiency of the new results.

Solutions of Fractional differential equations with some modifications of Adomian Decomposition method

المجلة: Delta University Scientific Journal

سنة النشر: 2023

تاريخ النشر: 2023-04-01

In this paper, we apply the Adomian decomposition method (ADM) for solving Fractional Differential Equations (FDEs) with some modifications to the traditional method. The aim of this paper is to make ADM more efficient, rapid in convergence, and easy to use, so we will discuss two modifications. We use the reliable modification to simplify calculations. For difficulties in symbolic integration, we use a numerical implementation method. All these modifications were applied to the integer-order case, so we would apply it to FDEs. Some numerical results are given from solving these cases and comparing the solution with the ADM method.

Semi-analytic solutions of nonlinear multidimensional fractional differential equations

المجلة: Math. Biosci. Eng

سنة النشر: 2022

تاريخ النشر: 2022-01-01

In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.

Solution of the SIR epidemic model of arbitrary orders containing Caputo-Fabrizio, Atangana-Baleanu and Caputo derivatives

المجلة: AIMS Mathematics

سنة النشر: 2024

تاريخ النشر: 2024-05-31

The main aim of this study was to apply an analytical method to solve a nonlinear system of fractional differential equations (FDEs). This method is the Adomian decomposition method (ADM), and a comparison between its results was made by using a numerical method: Runge-Kutta 4 (RK4). It is proven that there is a unique solution to the system. The convergence of the series solution is given, and the error estimate is also proven. After that, the susceptible-infected-recovered (SIR) model was taken as an real phenomenon with such systems. This system is discussed with three different fractional derivatives (FDs): the Caputo-Fabrizio derivative (CFD), the Atangana-Baleanu derivative (ABD), and the Caputo derivative (CD). A comparison between these three different derivatives is given. We aimed to see which one of the new definitions (ABD and CFD) is close to one of the most important classical definitions (CD).

Solutions of Nonlinear Fractional Differential Equations with Nondifferentiable Terms

المجلة: Mathematics and Statistics

سنة النشر: 2022

تاريخ النشر: 2022-08-20

In this research, we employ a newly developed strategy based on a modified version of the Adomian decomposition method (ADM) to solve nonlinear fractional differential equations (FDE) with both differential and nondifferential variables. FDE have disturbed the interest of many researchers. This is due to the development of both the theory and applications of fractional calculus. This track from various areas of fractional differential equations can be used to model various fields of science and engineering such as fluid flows, viscoelasticity, electrochemistry, control, electromagnetic, and many others. Several fractional derivative definitions have been presented, including Riemann–Liouville, Caputo,and Caputo– Fabrizio fractional derivative. We just need to calculate the first Adomain polynomial in this technique avoiding the hurdles in the nondifferentiable nonlinear terms’ remaining polynomials. Furthermore, the proposed technique is easy to programme and produces the desired output with minimal work and time on the same processor. When compared to the exact solution, this method has the advantage of reducing calculation steps, while producing accurate results. The supporting evidence proves that modified Adomian decomposition has an advantage over traditional Adomian decomposition method which can be explained very clear with nonlinear fractional differential equations. Our computational examples with difficult issues are used to prove the new algorithm’s efficiency. The results show that the modified ADM is powerful, which has a faster convergence solution than the original one. Convergence analysis is discussed, also the uniqueness is explained.