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Numerical Solution of Troesch’s Problem by Sinc-Collocation Method

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Applied Mathematics 2013年第4期4卷 707-712页

作者： mohamed el-gamel Department of Mathematical Sciences Faculty of Engineering Mansoura University Mansoura Egypt

A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.

关键词： Sinc Function Collocation Method Troesch’s Problem Numerical Solution

An Efficient Technique for Finding the Eigenvalues of Fourth-Order Sturm-Liouville Problems

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Applied Mathematics 2012年第8期3卷 920-925页

作者： mohamed el-gamel Mona Sameeh Department of Mathematical Sciences Faculty of Engineering Mansoura University Egypt

In this work, we present a computational method for solving eigenvalue problems of fourth-order ordinary differential equations which based on the use of Chebychev method. The efficiency of the method is demonstrated ... 详细信息

关键词： Chebychev Polynomial Fourth-Order Sturm-Liouville Eigenvalue

A Robust and Effective Method for Solving Two-Point BVP in Modelling Viscoelastic Flows

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Applied Mathematics 2020年第1期11卷 23-34页

作者： mohamed el-gamel Ola mohamed Neveen el-Shamy Department of Mathematical Sciences Faculty of Engineering Mansoura University Mansoura Egypt

Chebyshev collocation method is used to approximate solutions of two-point BVP arising in modelling viscoelastic flow. The scheme is tested on four nonlinear problems. The comparison with other methods is made. The re... 详细信息

关键词： Chebyshev Collocation Viscoelastic Flow Fifth-Order Nonlinear

Numerical Solutions for the Time-Dependent Emden-Fowler-Type Equations by B-Spline Method

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Applied Mathematics 2014年第4期5卷 593-600页

作者： mohamed el-gamel W. el-bashbashy Atallah el-Shenawy Department of Mathematical Sciences Faculty of Engineering Mansoura University Mansoura Egypt

A numerical method based on B-spline is developed to solve the time-dependent Emden-Fow- ler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point at x = 0. The error analysis of the method is described. Numerical results are given to illustrate the efficiency of the proposed method.

关键词： B-Spline Time-Dependent Numerical Solutions Emden-Fowler Type

Chelyshkov-Tau Approach for Solving Bagley-Torvik Equation

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Applied Mathematics 2017年第12期8卷 1795-1807页

作者： mohamed el- gamel Mahmoud Abd-el-Hady Magdy el-Azab Department of Mathematical Sciences Faculty of Engineering Mansoura University Mansoura Egypt

There are few numerical techniques available to solve the Bagley-Torvik equation which occurs considerably frequently in various offshoots of applied mathematics and mechanics. In this paper, we show that Chelyshkov-tau method is a very effective tool in numerically solving this equation. To show the accuracy and the efficiency of the method, several problems are implemented and the comparisons are given with other methods existing in the recent literature. The results of numerical tests confirm that Chelyshkov-tau method is superior to other existing ones and is highly accurate.

关键词： Chelyshkov Tau Method Bagley-Torvik Caputo Derivative Residual Functions

Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions

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Applied Mathematics 2022年第2期13卷 101-119页

作者： mohamed el-gamel Galal I. el-Baghdady Mahmoud Abd el-Hady Department of Mathematical Sciences Faculty of Engineering Mansoura University Egypt

In this work, a highly efficient algorithm is developed for solving the parabolic partial differential equation (PDE) with the nonlocal condition. For this purpose, we employ orthogonal Chelyshkov polynomials as the basis. The convergence analysis of the proposed scheme is derived. Numerical experiments are carried out to explain the efficiency and precision of the proposed scheme. Furthermore, the reliability of the scheme is verified by comparisons with assured existing methods.

关键词： Chelyshkov Collocation Method Parabolic Nonlocal Boundary Conditions

Two Very Accurate and Efficient Methods for Solving Time-Dependent Problems

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Applied Mathematics 2018年第11期9卷 1270-1280页

作者： mohamed el-gamel Waleed Adel M. S. el-Azab Department of Mathematical Sciences Faculty of Engineering Mansoura University Mansoura Egypt

In this paper, collocation method based on Bernoulli and Galerkin method based on wavelet are proposed for solving nonhomogeneous heat and wave equations. The two methods have the linear systems solved by suitable sol... 详细信息

关键词： Wavelet Galerkin Daubechies Bernoulli Collocation

Optimizing Grey Wolf Optimization: A Novel Agents’ Positions Updating Technique for Enhanced Efficiency and Performance

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Open Journal of Optimization 2024年第1期13卷 21-30页

作者： Mahmoud Khatab mohamed el-gamel Ahmed I. Saleh Asmaa H. Rabie Atallah el-Shenawy Department of Mathematics and Engineering Physics Faculty of Engineering Mansoura University Mansoura Egypt Department of Computers and Control Faculty of Engineering Mansoura University Mansoura Egypt Department of Mathematics Faculty of Science New Mansoura University Mansoura Egypt

Grey Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm that has gained popularity for solving optimization problems. In GWO, the success of the algorithm heavily relies on the efficient updating of the agents’ positions relative to the leader wolves. In this paper, we provide a brief overview of the Grey Wolf Optimization technique and its significance in solving complex optimization problems. Building upon the foundation of GWO, we introduce a novel technique for updating agents’ positions, which aims to enhance the algorithm’s effectiveness and efficiency. To evaluate the performance of our proposed approach, we conduct comprehensive experiments and compare the results with the original Grey Wolf Optimization technique. Our comparative analysis demonstrates that the proposed technique achieves superior optimization outcomes. These findings underscore the potential of our approach in addressing optimization challenges effectively and efficiently, making it a valuable contribution to the field of optimization algorithms.

关键词： Grey Wolf Optimization (GWO) Metaheuristic Algorithm Optimization Problems Agents’ Positions Leader Wolves Optimal Fitness Values Optimization Challenges

Effects of P301L-TAU on post-translational modifications of microtubules in human iPSC-derived cortical neurons and TAU transgenic mice

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Neural Regeneration Research 2025年第8期20卷 2348-2360页

作者： mohamed Aghyad Al Kabbani Christoph Köhler Hans Zempel Institute of Human Genetics Faculty of Medicine and University Hospital CologneUniversity of CologneCologneGermany Center for Molecular Medicine Cologne(CMMC) University of CologneCologneGermany Center Anatomy Department ⅡMedical FacultyUniversity of CologneCologneGermany

TAU is a microtubule-associated protein that promotes microtubule assembly and stability in the *** is missorted and aggregated in an array of diseases known as *** are essential for neuronal function and regulated via a complex set of post-translational modifications,changes of which affect microtubule stability and dynamics,microtubule interaction with other proteins and cellular structures,and mediate recruitment of microtubule-severing *** impairment of microtubule dynamics causes neuronal dysfunction,we hypothesize cognitive impairment in human disease to be impacted by impairment of microtubule *** therefore aimed to study the effects of a disease-causing mutation of TAU(P301L)on the levels and localization of microtubule post-translational modifications indicative of microtubule stability and dynamics,to assess whether P301L-TAU causes stability-changing modifications to *** investigate TAU localization,phosphorylation,and effects on tubulin post-translational modifications,we expressed wild-type or P301L-TAU in human MAPT-KO induced pluripotent stem cell-derived neurons(i Neurons)and studied TAU in neurons in the hippocampus of mice transgenic for human P301L-TAU(p R5 mice).Human neurons expressing the longest TAU isoform(2N4R)with the P301L mutation showed increased TAU phosphorylation at the AT8,but not the p-Ser-262 epitope,and increased polyglutamylation and acetylation of microtubules compared with endogenous TAU-expressing neurons.P301L-TAU showed pronounced somatodendritic presence,but also successful axonal enrichment and a similar axodendritic distribution comparable to exogenously expressed 2N4R-wildtype-TAU.P301L-TAU-expressing hippocampal neurons in transgenic mice showed prominent missorting and tauopathy-typical AT8-phosphorylation of TAU and increased polyglutamylation,but reduced acetylation,of microtubules compared with non-transgenic *** sum,P301L-TAU results in changes in micr

关键词： human induced pluripotent stem cell microtubules P301L pR5 mice TAU tauopathy tubulin code