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bsj-2624
Solution of Nonlinear High Order Multi-Point Boundary Value Problems By Semi-Analytic Technique
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In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.

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Publication Date
Tue Aug 01 2023
Journal Name
Baghdad Science Journal
The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems
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In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

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Publication Date
Tue Jun 01 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
A New Approach of Morgan-Voyce Polynomial to Solve Three Point Boundary Value Problems
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In this paper, a new procedure is introduced to estimate the solution for the three-point boundary value problem which is instituted on the use of Morgan-Voyce polynomial. In the beginning, Morgan-Voyce polynomial along with their important properties is introduced. Next, this polynomial with aid of the collocation method utilized to modify the differential equation with boundary conditions to the algebraic system. Finally, the examples approve the validity and accuracy of the proposed method.

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Publication Date
Fri Apr 21 2023
Journal Name
Aip Conference Proceedings
Efficient computational methods for solving the nonlinear initial and boundary value problems
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In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

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Publication Date
Mon Jul 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Continuous Classical Optimal Control Problems for Triple Nonlinear Elliptic Boundary Value Problem
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     In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of

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Publication Date
Wed Jan 01 2020
Journal Name
Arab Journal Of Basic And Applied Sciences
Boundary-domain integral method and homotopy analysis method for systems of nonlinear boundary value problems in environmental engineering
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Publication Date
Tue Jan 01 2019
Journal Name
Science International.(lahore)
GALERKIN'S METHOD TO SOLVE THE LINEAR SECOND ORDER DELAY MULTI-VALUE PROBLEMS
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Publication Date
Wed Jul 20 2022
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems with State Vector Constraints
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This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

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Publication Date
Tue Nov 13 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Approximation Solution of a Nonlinear Parabolic Boundary Value Problem Via Galerkin Finite Elements Method with Crank-Nicolson
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    This paper deals with finding the approximation solution of a nonlinear parabolic boundary value problem (NLPBVP) by using the Galekin finite element method (GFEM) in space and Crank Nicolson (CN) scheme in time, the problem then reduce to solve a Galerkin nonlinear algebraic system(GNLAS). The predictor and the corrector technique (PCT) is applied here to solve the GNLAS, by transforms it to a Galerkin linear algebraic system (GLAS). This GLAS is solved once using the Cholesky method (CHM) as it appear in the matlab package and once again using the Cholesky reduction order technique (CHROT) which we employ it here to save a massive time. The results, for CHROT are given by tables and figures and show

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Publication Date
Sun Mar 04 2018
Journal Name
Iraqi Journal Of Science
Improved High order Euler Method for Numerical Solution of Initial value Time- Lag Differential Equations
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The goal of this paper is to expose a new numerical method for solving initial value time-lag of delay differential equations by employing a high order improving formula of Euler method known as third order Euler method. Stability condition is discussed in detail for the proposed technique. Finally some examples are illustrated to verify the validity, efficiency and accuracy of the method.

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Publication Date
Tue Oct 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method
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     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

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