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bsj-572
First Order Nonlinear Neutral Delay Differential Equations
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The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

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Publication Date
Sun Dec 02 2012
Journal Name
Baghdad Science Journal
Numerical Approach of Linear Volterra Integro-Differential Equations Using Generalized Spline Functions
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This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

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Publication Date
Mon Jan 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Continuous Classical Optimal Control Problems for Triple Elliptic Partial Differential Equations
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In this paper the Galerkin method is used to prove the existence and uniqueness theorem for the solution of the state vector of the triple linear elliptic partial differential equations for fixed continuous classical optimal control vector. Also, the existence theorem of a continuous classical optimal control vector related with the triple linear equations of elliptic types is proved. The existence of a unique solution for the triple adjoint equations related with the considered triple of the state equations is studied. The Fréchet derivative of the cost function is derived. Finally the theorem of necessary conditions for optimality of the considered problem is proved.

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Publication Date
Thu Apr 27 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Numerical Solutions Of The Nonlocal Problems For The Diffusion Partial Differential Equations
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    In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.

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Publication Date
Thu May 30 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Analytical approximate solutions of random integro differential equations with laplace decomposition method
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An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

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Publication Date
Thu Apr 27 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Existence and Uniqueness of The Solution of Nonlinear Volterra Fuzzy Integral Equations
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 In this paper, we proved the existence and uniqueness of the solution of nonlinear Volterra fuzzy integral equations of the second kind.
 

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Publication Date
Tue Sep 08 2020
Journal Name
Baghdad Science Journal
Matrix Form of Deriving High Order Schemes for the First Derivative
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For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated

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Publication Date
Thu Mar 06 2025
Journal Name
Aip Conference Proceedings
Solving 5th order nonlinear 4D-PDEs using efficient design of neural network
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Publication Date
Wed Jan 01 2020
Journal Name
Journal Of King Saud University - Science
Three iterative methods for solving second order nonlinear ODEs arising in physics
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Publication Date
Thu Sep 01 2022
Journal Name
Iaes International Journal Of Robotics And Automation
Implementation of a complex fractional order proportional-integral-derivative controller for a first order plus dead time system
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This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabi

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Publication Date
Mon May 14 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Generalized Spline Approach For Solving System of Linear Fractional Volterra Integro-Differential Equations
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    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

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