Salam J Majeed | Thi-Qar UNIVERSITY (original) (raw)

Papers by Salam J Majeed

Research paper thumbnail of The dynamics of an aquatic ecological model with aggregation, Fear and Harvesting Effects

AIMS Mathematics

In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feedin... more In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feeding fish and predatory fish model with aggregation effect of microcystis aeruginosa. Fear effect of predatory fish on filter feeding fish and harvesting effect of big fish is considered. Mathematical analysis includes two parts. The first is theoretical part, which includes proving the positive and constraining solutions of the model. Also finding equilibrium points and studying their local stability is included in this part. In addition, analyzing the local bifurcation of equilibrium points and indicating the type of bifurcation is discussed here. On the other hand, the second part contains the numerical simulation of all the theoretical results, where we compare the numerical values of the conditions obtained in the theoretical part.

Research paper thumbnail of Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator

Chaos, Solitons & Fractals

Research paper thumbnail of Qualitative Analysis and Traveling wave Solutions for the Nonlinear Convection Equations with Absorption

Journal of Physics: Conference Series, 2020

We discuss qualitative behavior of the solutions for the nonlinear parabolic equation which model... more We discuss qualitative behavior of the solutions for the nonlinear parabolic equation which modeling nonlinear convection equation with absorption. This model represents the movement of growing population that is ruled by convection process. In this paper, we concentrate on proving the existence of traveling wave solutions for the nonlinear convection-reaction equations. In addition, we consider the model when the speed of advective wave may breakdown and the problem has a shock wave solution. The mathematical interesting of the waves comes from the behaviors of singular differential equation and discussing the stability of the solution.

Research paper thumbnail of Easy Numerical Method to Solution a System of Linear Volterra Integral Equations

Journal of Al-Nahrain University Science, 2011

Research paper thumbnail of The dynamics of an Omnivore-predator-prey model with harvesting and two different nonlinear functional responses

AIP Conference Proceedings, 2019

Research paper thumbnail of Numerical Methods for Solving Linear Fredholmvolterra Integral Equations

Journal of Al-Nahrain University Science, 2008

The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral ... more The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral equations of the first and second kinds. These methods namely are the repeated Trapezoidal method and the repeated Simpson's 1/3 method. Numerical examples are presented to show the efficiency and accuracy of the presented work.

Research paper thumbnail of The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

International Journal of Differential Equations, 2016

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. I... more We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

Research paper thumbnail of Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind

American Journal of Applied Mathematics, 2014

In this paper numerical solution to system of linear Fredholm integral equations by modified midp... more In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.

Research paper thumbnail of Solutions for Linear Fredholm-Voltterra Integral Equations of the Second Kind Using the Repeated Corrected Trapezoidal and Simpson S Methods

Journal of Al-Nahrain University Science, 2010

In this paper we introduce numerical methods for solving linear Fredholm Volterra integral equati... more In this paper we introduce numerical methods for solving linear Fredholm Volterra integral equations of the second kind. The main idea is based on the corrected trapezoidal and Simpson s 1/3 quadrature formulas. These techniques are very effective. Numerical results are illustrated by different examples.

Research paper thumbnail of The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

Iranian Journal of Mathematical Sciences and Informatics, 2020

A mathematical model describing the dynamics of a delayed stage structure prey-predator system wi... more A mathematical model describing the dynamics of a delayed stage structure prey-predator system with prey refuge is considered. The existence, uniqueness and boundedness of the solution are discussed. All the feasible equilibrium points are determined. The stability analysis of them are investigated. By employing the time delay as the bifurcation parameter, we observed the existence of Hopf bifurcation at the positive equilibrium. The stability and direction of the Hopf bifurcation are determined by utilizing the normal form method and the center manifold reduction. Numerical simulations are given to support the analytic results.

Research paper thumbnail of Adapted Method for Solving Linear Voltterra Integral Equations of the Second kind Using Corrected Simpson's Rule

In this paper, we present an adapted method for solving linear Volterra integral equations of the... more In this paper, we present an adapted method for solving linear Volterra integral equations of the second kind with regular kernel. This method is based on the corrected Simpson's rule. Numerical examples are given to prove the efficiency and accuracy of our method by comparison with known methods.

Research paper thumbnail of Some Estimates to Best Approximation of Functions by Fourier-Jacobi Differential Operators

IOP Conference Series: Materials Science and Engineering

Research paper thumbnail of NUMERICAL METHODS FOR SOLVING LINEAR FREDHOLM- VOLTERRA INTEGRAL EQUATIONS

The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral ... more The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral equations of the first and second kinds. These methods namely are the repeated Trapezoidal method and the repeated Simpson's 1/3 method. Numerical examples are presented to show the efficiency and accuracy of the presented work.

Research paper thumbnail of Easy Numerical Method to Solution a System of Linear Volterra Integral Equations

In this paper, we present an adapted method for solving systems of linear Volterra ... more In this paper, we present an adapted method for solving systems of linear Volterra integral equations of the second kind. This method is based on the Simpson's rule. We used two numerical examples to show the accuracy and simple of our method by comparison with known methods.

Research paper thumbnail of The dynamics of an aquatic ecological model with aggregation, Fear and Harvesting Effects

AIMS Mathematics

In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feedin... more In this paper, we investigate an aquatic ecological model of microcystis aeruginosa-filter feeding fish and predatory fish model with aggregation effect of microcystis aeruginosa. Fear effect of predatory fish on filter feeding fish and harvesting effect of big fish is considered. Mathematical analysis includes two parts. The first is theoretical part, which includes proving the positive and constraining solutions of the model. Also finding equilibrium points and studying their local stability is included in this part. In addition, analyzing the local bifurcation of equilibrium points and indicating the type of bifurcation is discussed here. On the other hand, the second part contains the numerical simulation of all the theoretical results, where we compare the numerical values of the conditions obtained in the theoretical part.

Research paper thumbnail of Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator

Chaos, Solitons & Fractals

Research paper thumbnail of Qualitative Analysis and Traveling wave Solutions for the Nonlinear Convection Equations with Absorption

Journal of Physics: Conference Series, 2020

We discuss qualitative behavior of the solutions for the nonlinear parabolic equation which model... more We discuss qualitative behavior of the solutions for the nonlinear parabolic equation which modeling nonlinear convection equation with absorption. This model represents the movement of growing population that is ruled by convection process. In this paper, we concentrate on proving the existence of traveling wave solutions for the nonlinear convection-reaction equations. In addition, we consider the model when the speed of advective wave may breakdown and the problem has a shock wave solution. The mathematical interesting of the waves comes from the behaviors of singular differential equation and discussing the stability of the solution.

Research paper thumbnail of Easy Numerical Method to Solution a System of Linear Volterra Integral Equations

Journal of Al-Nahrain University Science, 2011

Research paper thumbnail of The dynamics of an Omnivore-predator-prey model with harvesting and two different nonlinear functional responses

AIP Conference Proceedings, 2019

Research paper thumbnail of Numerical Methods for Solving Linear Fredholmvolterra Integral Equations

Journal of Al-Nahrain University Science, 2008

The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral ... more The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral equations of the first and second kinds. These methods namely are the repeated Trapezoidal method and the repeated Simpson's 1/3 method. Numerical examples are presented to show the efficiency and accuracy of the presented work.

Research paper thumbnail of The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

International Journal of Differential Equations, 2016

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. I... more We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

Research paper thumbnail of Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind

American Journal of Applied Mathematics, 2014

In this paper numerical solution to system of linear Fredholm integral equations by modified midp... more In this paper numerical solution to system of linear Fredholm integral equations by modified midpoint method is considered. This method transforms the system of linear Fredholm integral equations into a system of linear algebraic equations that can be solved easily with any of the usual methods. Finally, some illustrative examples are presented to test this method and the results reveal that this method is very effective and convenient by comparison with exact solution and with other numerical methods such as midpoint method, trapezoidal method, Simpson's method and modified trapezoidal method. All results are computed by using a programs written in Matlab R2012b.

Research paper thumbnail of Solutions for Linear Fredholm-Voltterra Integral Equations of the Second Kind Using the Repeated Corrected Trapezoidal and Simpson S Methods

Journal of Al-Nahrain University Science, 2010

In this paper we introduce numerical methods for solving linear Fredholm Volterra integral equati... more In this paper we introduce numerical methods for solving linear Fredholm Volterra integral equations of the second kind. The main idea is based on the corrected trapezoidal and Simpson s 1/3 quadrature formulas. These techniques are very effective. Numerical results are illustrated by different examples.

Research paper thumbnail of The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

Iranian Journal of Mathematical Sciences and Informatics, 2020

A mathematical model describing the dynamics of a delayed stage structure prey-predator system wi... more A mathematical model describing the dynamics of a delayed stage structure prey-predator system with prey refuge is considered. The existence, uniqueness and boundedness of the solution are discussed. All the feasible equilibrium points are determined. The stability analysis of them are investigated. By employing the time delay as the bifurcation parameter, we observed the existence of Hopf bifurcation at the positive equilibrium. The stability and direction of the Hopf bifurcation are determined by utilizing the normal form method and the center manifold reduction. Numerical simulations are given to support the analytic results.

Research paper thumbnail of Adapted Method for Solving Linear Voltterra Integral Equations of the Second kind Using Corrected Simpson's Rule

In this paper, we present an adapted method for solving linear Volterra integral equations of the... more In this paper, we present an adapted method for solving linear Volterra integral equations of the second kind with regular kernel. This method is based on the corrected Simpson's rule. Numerical examples are given to prove the efficiency and accuracy of our method by comparison with known methods.

Research paper thumbnail of Some Estimates to Best Approximation of Functions by Fourier-Jacobi Differential Operators

IOP Conference Series: Materials Science and Engineering

Research paper thumbnail of NUMERICAL METHODS FOR SOLVING LINEAR FREDHOLM- VOLTERRA INTEGRAL EQUATIONS

The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral ... more The aim of this work is to use some numerical methods to solve linear Fredholm-Volterra integral equations of the first and second kinds. These methods namely are the repeated Trapezoidal method and the repeated Simpson's 1/3 method. Numerical examples are presented to show the efficiency and accuracy of the presented work.

Research paper thumbnail of Easy Numerical Method to Solution a System of Linear Volterra Integral Equations

In this paper, we present an adapted method for solving systems of linear Volterra ... more In this paper, we present an adapted method for solving systems of linear Volterra integral equations of the second kind. This method is based on the Simpson's rule. We used two numerical examples to show the accuracy and simple of our method by comparison with known methods.