Mohammed Alshbool
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View article: Computational Method to Find Solutions of Mathematical Problems with Error and Stability Analysis
Computational Method to Find Solutions of Mathematical Problems with Error and Stability Analysis Open
This paper provides stability theorems and residual correction procedures for a realistic optimization problem using an accurate computational method. An example illustration has shown optimal performance with high-accuracy orders.
View article: Review of: "A Description of the Melting of Ice With the Modified Clapeyron–Clausius Equation"
Review of: "A Description of the Melting of Ice With the Modified Clapeyron–Clausius Equation" Open
Potential competing interests: No potential competing interests to declare.1-In general, a good paper, he needs to add some parts to the literature review.2-The author should write and explain more about the Clapeyron-Clausius Equation 3-H…
View article: Bernstein polynomials method for solving multi-order fractional neutral pantograph equations with error and stability analysis
Bernstein polynomials method for solving multi-order fractional neutral pantograph equations with error and stability analysis Open
In this investigation, we present a new method for addressing fractional neutral pantograph problems, utilizing the Bernstein polynomials method. We obtain solutions for the fractional pantograph equations by employing operational matrices…
View article: Implementing Bernstein Operational Matrices to Solve a Fractional‐Order Smoking Epidemic Model
Implementing Bernstein Operational Matrices to Solve a Fractional‐Order Smoking Epidemic Model Open
This paper leverages the Bernstein operational matrices method for the first time in order to resolve the nonlinear fractional smoking epidemic model presented in terms of Caputo’s fractional derivative. An approximate solution is derived …
View article: Fractional Bernstein operational matrices for solving integro-differential equations involved by Caputo fractional derivative
Fractional Bernstein operational matrices for solving integro-differential equations involved by Caputo fractional derivative Open
The present work is devoted to developing two numerical techniques based on fractional Bernstein polynomials, namely fractional Bernstein operational matrix method, to numerically solving a class of fractional integro-differential equation…
View article: A Novel Numerical Method for Solving Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral Equations with Zero Absolute Error
A Novel Numerical Method for Solving Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral Equations with Zero Absolute Error Open
In this work, a new numerical method for the fractional diffusion-wave equation and nonlinear Fredholm and Volterra integro-differential equations is proposed. The method is based on Euler wavelet approximation and matrix inversion of an M…
View article: A computational model for hybrid nanofluid flow on a rotating surface in the existence of convective condition
A computational model for hybrid nanofluid flow on a rotating surface in the existence of convective condition Open
The current work aims to study heat transfer properties within the flow. A newly developed idea regarding hybrid nanofluid is utilized to obtain the desired outcomes. This study focused on hybrid base nano liquid flow past an exponentially…
View article: Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations
Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations Open
In this study, we propose an extension of the modified Newton-Househölder methods to find multiple roots with unknown multiplicity of nonlinear equations. With four functional evaluations per iteration, the proposed method achieves an opti…
View article: Heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface
Heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface Open
The present study investigates the rate of heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface subject to the heat generation/absorption and mass suction. The analysis has been carried ou…
View article: Fractional Bernstein Series Solution of Fractional Diffusion Equations with Error Estimate
Fractional Bernstein Series Solution of Fractional Diffusion Equations with Error Estimate Open
In the present paper, we introduce the fractional Bernstein series solution (FBSS) to solve the fractional diffusion equation, which is a generalization of the classical diffusion equation. The Bernstein polynomial method is a promising on…
View article: Bernstein Polynomials Method to Solve Fractional Model of Basic Enzyme Kinetics
Bernstein Polynomials Method to Solve Fractional Model of Basic Enzyme Kinetics Open
Approximate solutions of fractional model of biochemical reaction using Bernstein polynomials method are derived in this paper.Enzyme-substrate reaction system is formed by a system of nonlinear ordinary differential equations.Fractional o…
View article: Residual Correction Procedure with Bernstein Polynomials for Solving Important Systems of Ordinary Differential Equations
Residual Correction Procedure with Bernstein Polynomials for Solving Important Systems of Ordinary Differential Equations Open
One of the most attractive subjects in applied sciences is to obtain exact or approximate solutions for different types of linear and nonlinear systems. Systems of ordinary differential equations like systems of second-or... | Find, read a…
View article: Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations
Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations Open
In this paper, we adapt for the first time the operational matrices of Bernstein polynomials method for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting th…
View article: Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions
Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions Open
An algorithm for approximating solutions to fractional differential equations (FDEs) in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1) in the operational matrices of Bernstein polynomials, the fractional Berns…
View article: Multistage Bernstein polynomials for the solutions of the Fractional Order Stiff Systems
Multistage Bernstein polynomials for the solutions of the Fractional Order Stiff Systems Open
In this paper, a new modification of the Bernstein polynomials method called Multistage Bernstein polynomials (MB-polynomials) is applied to solve new topic, which is Fractional Order Stiff Systems. The MB-polynomials is a simple reliable …
View article: APPROXIMATE SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH ESTIMATION ERROR BY USING BERNSTEIN POLYNOMIALS
APPROXIMATE SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH ESTIMATION ERROR BY USING BERNSTEIN POLYNOMIALS Open
We present an approximate solution depending on collocation method and Bernstein polynomials for numerical solution of a singular nonlinear differential equations with the mixed conditions.The method is given with two different priori erro…