A reliable iterative method for solving Volterra integro-differential equations and some applications for the Lane–Emden equations of the first kind
(7)
Publication Date
Thu Jan 01 2015
Journal Name
Journal Of The College Of Basic Education
Efficient Modifications of the Adomian Decomposition Method for Thirteenth Order Ordinary Differential Equations
Modification adomian decomposition method
Boundary value
problems
Linear and Nonlinear Problems
Approximate Solution.
This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.
Publication Date
Sun Dec 01 2024
Journal Name
Baghdad Science Journal
Bernoulli Polynomials Method for Solving Integral Equations with Singular Kernel
هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة
... Show More
Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Oscillation of Nonlinear First Order Neutral Differential Equations
In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.
Publication Date
Sat Oct 01 2022
Journal Name
Journal Of Computational Science
(30)
Publication Date
Sat Oct 01 2022
Journal Name
Journal Of Computational Science
(30)
Publication Date
Sun Jul 01 2018
Journal Name
Computers & Mathematics With Applications
(23)
Publication Date
Wed May 13 2020
Journal Name
Nonlinear Engineering
Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences
Abstract<p>In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using <italic>Mathematica</italic>® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To ill</p>
... Show More
(10)
Publication Date
Wed May 13 2020
Journal Name
Nonlinear Engineering
Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences
Abstract<p>In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using <italic>Mathematica</italic>® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To ill</p>
... Show More
(15)
(10)
Publication Date
Tue Feb 01 2022
Journal Name
Baghdad Science Journal
Solving Whitham-Broer-Kaup-Like Equations Numerically by using Hybrid Differential Transform Method and Finite Differences Method
Differential Transform Method
Finite Differences Method
Hybrid Differential Transform - Finite Differences Method
Whitham-Broer-Kaup-Like Equations
This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.
(5)
(3)
Publication Date
Mon Jan 04 2021
Journal Name
Iium Engineering Journal
RELIABLE ITERATIVE METHODS FOR SOLVING 1D, 2D AND 3D FISHER’S EQUATION
In the present paper, three reliable iterative methods are given and implemented to solve the 1D, 2D and 3D Fisher’s equation. Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM) and Banach contraction method (BCM) are applied to get the exact and numerical solutions for Fisher's equations. The reliable iterative methods are characterized by many advantages, such as being free of derivatives, overcoming the difficulty arising when calculating the Adomian polynomial boundaries to deal with nonlinear terms in the Adomian decomposition method (ADM), does not request to calculate Lagrange multiplier as in the Variational iteration method (VIM) and there is no need to create a homotopy like in the Homotopy perturbation method (H
... Show More
(2)