M. Abdelhakem
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View article: Pseudo-spectral second kind Chebyshev polynomials differentiation matrices for solving high-order nonlinear differential equations
Pseudo-spectral second kind Chebyshev polynomials differentiation matrices for solving high-order nonlinear differential equations Open
New differentiation matrices (DMs) forms have been constructed using the pseudo-spectral method via the second kind of Chebyshev polynomials (SK-CHPs) as basis functions. For that purpose, firstly, we determined the Gauss-Lobatto quadratur…
View article: PSEUDOSPECTRAL FRACTIONAL DIFFERENTIATION MATRICES FOR SOLVING RICCATI AND BAGLEY–TORVIK FRACTIONAL MODELS VIA MIXED SHIFTED POLYNOMIALS
PSEUDOSPECTRAL FRACTIONAL DIFFERENTIATION MATRICES FOR SOLVING RICCATI AND BAGLEY–TORVIK FRACTIONAL MODELS VIA MIXED SHIFTED POLYNOMIALS Open
Two sets of basis functions have been developed by integrating shifted Chebyshev polynomials and Legendre polynomials. These functions primarily aim to create diverse forms of differentiation matrices using pseudospectral approximation tec…
View article: MONIC CHEBYSHEV’S FIRST DERIVATIVE PSEUDO-GALERKIN METHOD FOR SOLVING LINEAR AND NONLINEAR IBVPS: REAL-LIFE AND PHYSICAL APPLICATIONS
MONIC CHEBYSHEV’S FIRST DERIVATIVE PSEUDO-GALERKIN METHOD FOR SOLVING LINEAR AND NONLINEAR IBVPS: REAL-LIFE AND PHYSICAL APPLICATIONS Open
The computation of the solutions of differential equations (DEs) and integral equations (IEs) has noteworthy aspects due to the fact that these equations’ numerical or analytical solutions can yield applicable benefits in various realms of…
View article: Two modified shifted Chebyshev–Galerkin operational matrix methods for even-order partial boundary value problems
Two modified shifted Chebyshev–Galerkin operational matrix methods for even-order partial boundary value problems Open
This paper presents two operational matrices. The first one represents integer-order derivatives of the modified shifted Chebyshev polynomials of the second kind. These polynomials serve as basis functions in two spectral methods, Galerkin…
View article: Evaluation of Dynamic Multi-Leaf Collimator (MLC) versus Fixed MLC for Intensity Modulated Radiotherapy (IMRT) Using the Agility 160-Leaf Collimator
Evaluation of Dynamic Multi-Leaf Collimator (MLC) versus Fixed MLC for Intensity Modulated Radiotherapy (IMRT) Using the Agility 160-Leaf Collimator Open
The findings of this study indicate that dIMRT provides improved target coverage, homogeneity, and conformity while reducing treatment delivery time compared to ssIMRT.
View article: MHD 3D nanofluid flow over nonlinearly stretching/shrinking sheet with nonlinear thermal radiation: Novel approximation via Chebyshev polynomials’ derivative pseudo-Galerkin method
MHD 3D nanofluid flow over nonlinearly stretching/shrinking sheet with nonlinear thermal radiation: Novel approximation via Chebyshev polynomials’ derivative pseudo-Galerkin method Open
This research work aims to theoretically examine the influence of various factors on the three-dimensional nanofluid flow. The study includes parameters such as temperature ratio coefficient, Prandtl numbers, Schmidt, Soret, Dufour, Biot, …
View article: Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB
Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB Open
This study deals with ordinary differential equations and their solutions consuming effective numerical methods.We observing for more accurate numerical methods proximate to MATLAB solutions.Approaches are Adams-Bashforth and Rung-Kutta-4 …
View article: Solving some types of ordinary differential equations by using Chebyshev derivatives direct residual spectral method
Solving some types of ordinary differential equations by using Chebyshev derivatives direct residual spectral method Open
Herein, novel basis orthogonal polynomials have developed.These developed polynomials have been used to find the approximation solutions for some types of linear and non-linear ordinary differential equations by direct numerical method.Thi…
View article: Enhanced shifted Tchebyshev operational matrix of derivatives: two spectral algorithms for solving even-order BVPs
Enhanced shifted Tchebyshev operational matrix of derivatives: two spectral algorithms for solving even-order BVPs Open
Herein, new orthogonal polynomials have been generated from shifted Chebyshev polynomials that fulfill a given set of homogeneous boundary conditions and the necessary formulae have been established. Moreover, an integer order derivative o…
View article: Brachytherapy Vs Stereotactic Body Radiotherapy: A Comparative Dosimetric Study in the Carcinoma of the Cervix
Brachytherapy Vs Stereotactic Body Radiotherapy: A Comparative Dosimetric Study in the Carcinoma of the Cervix Open
View article: SHIFTED LEGENDRE FRACTIONAL PSEUDO-SPECTRAL INTEGRATION MATRICES FOR SOLVING FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS AND ABEL’S INTEGRAL EQUATIONS
SHIFTED LEGENDRE FRACTIONAL PSEUDO-SPECTRAL INTEGRATION MATRICES FOR SOLVING FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS AND ABEL’S INTEGRAL EQUATIONS Open
Shifted Legendre polynomials (SLPs) with the Riemann–Liouville fractional integral operator have been used to create a novel fractional integration tool. This tool will be called the fractional shifted Legendre integration matrix (FSL B-ma…
View article: Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems
Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems Open
A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation ma…
View article: Pseudo-spectral matrices as a numerical tool for dealing BVPs, based on Legendre polynomials’ derivatives
Pseudo-spectral matrices as a numerical tool for dealing BVPs, based on Legendre polynomials’ derivatives Open
The pseudo-spectral method is used as a technique to employ the first derivative of the well-known Legendre polynomials (FDLs) as novel basis functions. Then, the FDLs Gauss- Lobatto quadrature weights (FDLs-GLQWs) and zeros (FDLs-GLQZs) h…
View article: An efficient technique for approximated BVPs via the second derivative Legendre polynomials pseudo-Galerkin method: Certain types of applications
An efficient technique for approximated BVPs via the second derivative Legendre polynomials pseudo-Galerkin method: Certain types of applications Open
View article: Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems
Monic Chebyshev pseudospectral differentiation matrices for higher-order IVPs and BVPs: applications to certain types of real-life problems Open
View article: Thermal Flux and Magnetic Field Effects on Nano-fluids Over Shrinking/Stretching Sheet
Thermal Flux and Magnetic Field Effects on Nano-fluids Over Shrinking/Stretching Sheet Open
The motivation for studying nanofluid behavior under the influence of various external forces stems from its numerous applications in a variety of engineering industries.This paper focuses on the effect of a magnetic field and heat flux on…
View article: Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method
Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method Open
An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis o…
View article: Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations
Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations Open
The purpose of this paper is to show and explain a new formula that indicates with finality the derivatives of Shifted Monic Ultraspherical polynomials (SMUPs) of any degree and for any fractional-order using the shifted Monic Ultraspheric…
View article: Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems
Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems Open
View article: Spectral Monic Chebyshev Approximation for Higher Order Differential Equations
Spectral Monic Chebyshev Approximation for Higher Order Differential Equations Open
This paper is focused on performing a new method for solving linear and\nnonlinear higher-order boundary value problems (HBVPs). This direct numerical\nmethod based on spectral method. The trial function of this method is the Monic\nChebys…