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Search Results: 1 - 10 of 401495 matches for " M. M. Khader "
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Numerical Simulation Using GEM for the Optimization Problem as a System of FDEs  [PDF]
Mohamed Adel, Mohamed M. Khader
Applied Mathematics (AM) , 2017, DOI: 10.4236/am.2017.812126
In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fractional derivatives in these equations are in the Caputo sense. We compare our numerical solutions with those numerical solutions using RK4 method. The obtained numerical results of the optimization problem model show the simplicity and the efficiency of the proposed scheme.
Approximate Technique for Solving Class of Fractional Variational Problems  [PDF]
Emad M. Solouma, Mohamed M. Khader
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.65078
Abstract: This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show the simplicity and the efficiency of the proposed method.
The Impact of Clay Loading on the Relative Intercalation of Poly(Vinyl Alcohol)-Clay Composites  [PDF]
Moustafa M. Zagho, Mahmoud M. Khader
Journal of Materials Science and Chemical Engineering (MSCE) , 2016, DOI: 10.4236/msce.2016.410003
Abstract: Polymer clay nanocomposites (PCN) materials are industrially applied because of their unique properties. However many of their physical and chemical properties have not been determined. The formed structures of polymer/clay nanocomposite depend on the nature of interactions between polymer chains and clay platelets. According to the possible modes of interactions between polymer matrix and clay sheets, these nanocomposites can be classified into: intercalated, flocculated and exfoliated nanocomposites. In this work, the morphology of the nanocomposite was studied using X-ray diffraction (XRD) and nanoscaning electron microscopy (NSEM). XRD and NSEM measurements confirmed the intercalation between poly(vinyl alcohol) chains and cloisite® 20A sheets. Because of the intercalation between the clay platelets and the PVA chains, as the clay concentration increases as the band intensities in FT-IR spectra increase. On the other hand, the XRD did not provide clear shift of any of the clay peaks for PVA/cloisite®?10A nanocomposites and confirm the non-intercalation between PVA matrix and cloisite® 10A platelets. The relative intercalation (RI) of PVA/Cloisite® 20A nanocomposites declined with increase in the clay loadings. In contrast, for PVA/Cloisite® 10A, RI values slightly increased with increasing the clay loading.
An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations  [PDF]
M. M. Khader, A. M. S. Mahdy, M. M. Shehata
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.515228

In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations using Newton iteration method. We give numerical results to satisfy the accuracy and the applicability of the proposed schemes.

Chebyshev Pseudo-Spectral Method for Solving Fractional Advection-Dispersion Equation  [PDF]
N. H. Sweilam, M. M. Khader, M. Adel
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.519301
Abstract: Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution.
Numerical Solution for the Fractional Wave Equation Using Pseudo-Spectral Method Based on the Generalized Laguerre Polynomials  [PDF]
Nasser H. Sweilam, Mohamed M. Khader, Mohamed Adel
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.64058
Abstract: In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. The properties of Laguerre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which is solved by the finite difference method. An approximate formula of the fractional derivative is given. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. Numerical solutions of FWE are given and the results are compared with the exact solution.
Adsorption of CO2 on Polyethyleneimine 10k—Mesoporous silica Sorbent: XPS and TGA Studies  [PDF]
M. M. Khader, M. J. Al-Marri, Sardar Ali, G. Qi, E. P. Giannelis
American Journal of Analytical Chemistry (AJAC) , 2015, DOI: 10.4236/ajac.2015.64026
Abstract: A CO2 solid sorbent based on polyethyleneimine 10k (PEI-10k) impregnated into mesoporous silica (MPS) foam was synthesized and utilized to capture CO2 at temperatures ranged from 65°C to 95°C. The calculated nitrogen and carbon contents in the bulk of the PEI-10k/MPS sorbent were similar to the XPS results measured on the surface of the foam, suggesting that the PEI was homo-geneously distributed throughout the MPS support. After CO2 adsorptionthe N 1s peak was broadened and could be resolved into two components: a high binding energy component (~401 eV) and a lower binding energy one (396 eV), respectively. The former nitrogen states are consistent with a protonated amine, presumably, due to carbamate formation. The lower binding energy component (~396 eV) could possibly be due to strongly chemisorbed CO2. The maximum sorption capacity was about 4 mmole CO2/g sorbent at 85°C and 1 bar. This capacity was doubled by raising the CO2 pressure to 24.95 bars. The adsorption results can be described by a Langmuir adsorption isotherm.
Numerical Study for Simulation the MHD Flow and Heat-Transfer Due to a Stretching Sheet on Variable Thickness and Thermal Conductivity with Thermal Radiation  [PDF]
Mohamed M. Khader, Mohammed M. Babatin, Ali Eid, Ahmed M. Megahed
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.612180
Abstract: The main aim of this article is to introduce the approximate solution for MHD flow of an electrically conducting Newtonian fluid over an impermeable stretching sheet with a power law surface velocity and variable thickness in the presence of thermal-radiation and internal heat generation/absorption. The flow is caused by the non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The obtaining PDEs are transformed into non-linear system of ODEs using suitable boundary conditions for various physical parameters. We use the Chebyshev spectral method to solve numerically the resulting system of ODEs. We present the effects of more parameters in the proposed model, such as the magnetic parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented, moreover, the local skin-friction and Nusselt numbers. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The obtained numerical results confirm that the introduced technique is powerful mathematical tool and it can be implemented to a wide class of non-linear systems appearing in more branches in science and engineering.
A decision tree model to estimate the value of information provided by a groundwater quality monitoring network
A. Khader,D. Rosenberg,M. McKee
Hydrology and Earth System Sciences Discussions , 2012, DOI: 10.5194/hessd-9-13805-2012
Abstract: Nitrate pollution poses a health risk for infants whose freshwater drinking source is groundwater. This risk creates a need to design an effective groundwater monitoring network, acquire information on groundwater conditions, and use acquired information to inform management. These actions require time, money, and effort. This paper presents a method to estimate the value of information (VOI) provided by a groundwater quality monitoring network located in an aquifer whose water poses a spatially heterogeneous and uncertain health risk. A decision tree model describes the structure of the decision alternatives facing the decision maker and the expected outcomes from these alternatives. The alternatives include: (i) ignore the health risk of nitrate contaminated water, (ii) switch to alternative water sources such as bottled water, or (iii) implement a previously designed groundwater quality monitoring network that takes into account uncertainties in aquifer properties, pollution transport processes, and climate (Khader and McKee, 2012). The VOI is estimated as the difference between the expected costs of implementing the monitoring network and the lowest-cost uninformed alternative. We illustrate the method for the Eocene Aquifer, West Bank, Palestine where methemoglobinemia is the main health problem associated with the principal pollutant nitrate. The expected cost of each alternative is estimated as the weighted sum of the costs and probabilities (likelihoods) associated with the uncertain outcomes resulting from the alternative. Uncertain outcomes include actual nitrate concentrations in the aquifer, concentrations reported by the monitoring system, whether people abide by manager recommendations to use/not-use aquifer water, and whether people get sick from drinking contaminated water. Outcome costs include healthcare for methemoglobinemia, purchase of bottled water, and installation and maintenance of the groundwater monitoring system. At current methemoglobinemia and bottled water costs of 150 $/person and 0.6 $/baby/day, the decision tree results show that the expected cost of establishing the proposed groundwater quality monitoring network exceeds the expected costs of the uninformed alternatives and there is not value to the information the monitoring system provides. However, the monitoring system will be preferred to ignoring the health risk or using alternative sources if the methemoglobinemia cost rises to 300 $/person or the bottled water cost increases to 2.3 $/baby/day. Similarly, the monitoring system has value if the system can more ac
Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays
N. H. Sweilam,M. M. Khader,A. M. S. Mahdy
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/764894
Abstract: A numerical method for solving the fractional-order logistic differential equation with two different delays (FOLE) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations. Special attention is given to study the convergence and the error estimate of the presented method. Numerical illustrations are presented to demonstrate utility of the proposed method. Chaotic behavior is observed and the smallest fractional order for the chaotic behavior is obtained. Also, FOLE is studied using variational iteration method (VIM) and the fractional complex transform is introduced to convert fractional Logistic equation to its differential partner, so that its variational iteration algorithm can be simply constructed. Numerical experiment is presented to illustrate the validity and the great potential of both proposed techniques.
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