scholarly journals By using a new iterative method to the generalized system Zakharov-Kuznetsov and estimate the best parameters via applied the pso algorithm

2020 ◽  
Vol 19 (2) ◽  
pp. 1055 ◽  
Author(s):  
Abeer Aldabagh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Iterative Method ◽  
Numerical Method ◽  
Pso Algorithm ◽  
Accurate Solution ◽  
Generalized System ◽  
A New Technique ◽  
Best Parameters ◽  
New Iterative Method

In this paper, a new iterative method was applied to the Zakharov-Kuznetsov system to obtain the approximate solution and the results were close to the exact solution, A new technique has been proposed to reach the lowest possible error, and the closest accurate solution to the numerical method is to link the numerical method with the pso algorithm which is denoted by the symbol (NIM-PSO). The results of the proposed Technique showed that they are highly efficient and very close to the exact solution, and they are also of excellent effectiveness for treating partial differential equation systems.

scholarly journals The best parameters selection using pso algorithm to solving for ito system by new iterative technique

2020 ◽  
Vol 18 (3) ◽  
pp. 1638
Author(s):  
Karam Adel Abed ◽  
Abeer Abdulkhaleq Ahmad
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Approximate Solutions ◽  
Pso Algorithm ◽  
High Accuracy ◽  
Iterative Technique ◽  
Parameters Selection ◽  
A New Technique ◽  
Best Parameters ◽  
New Iterative Method

<p>The main aim of this study is to obtain the best approximate solution for the nonlinear Ito system by applying the new iterative method, A new technique has been proposed that combines the new iterative method with the particle optimization algorithm. The most important distinctive of this work is the analysis of errors between the exact solution of the system and the approximate solutions, which showed us that these approximate solutions of the proposed technique in particular have high accuracy because they converge significantly from the exact solution.</p>

scholarly journals An efficient new iterative method for oscillator differential equation

2012 ◽  
Vol 19 (6) ◽  
pp. 1473-1477 ◽  
Author(s):  
Yasir Khan ◽  
H. Vázquez-Leal ◽  
N. Faraz
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
New Iterative Method

Exact Two-Dimensional Theory of Spherical Spiral Groove Bearings

1980 ◽  
Vol 102 (4) ◽  
pp. 430-438 ◽  
Author(s):  
Susumu Murata ◽  
Yutaka Miyake ◽  
Nobuyoshi Kawabata
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Load Capacity ◽  
Perturbation Technique ◽  
Fluid Film ◽  
Two Dimensional ◽  
Spiral Groove ◽  
Dimensional Theory ◽  
New Iterative Method ◽  
Spiral Groove Bearing

This paper is concerned with a method of obtaining exact solution for the flow of fluid film of spherical spiral groove bearing. The problem is analyzed for three cases where the centers of two elements of a bearing coincide, slightly offset vertically and arbitrarily offset vertically. Effects of bearing parameters on the load capacity are examined. A perturbation technique is applied for the case of slight offset of centers of two spheres, and the stiffness is calculated. For the case of large offset, a new iterative method is developed in this paper.

scholarly journals New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma-Tasso-Olver Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Mohammad Jibran Khan ◽  
Rashid Nawaz ◽  
Samreen Farid ◽  
Javed Iqbal
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Fractional Order ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Order Solution ◽  
Differential Transform ◽  
New Iterative Method ◽  
Good Agreement

The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. Results obtained by the proposed method for different fractional-order derivatives are compared with those obtained by the fractional reduced differential transform method (FRDTM). The 2nd-order approximate solutions by the new iterative method are in good agreement with the exact solution as compared to the 5th-order solution by the FRDTM.

Numerical Solution to Volterra-Type Integro-Differential Equations of the Second Kinds by Legendre Collocation Method

2014 ◽  
Vol 687-691 ◽  
pp. 1522-1527
Author(s):  
Ting Jing Zhao
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Collocation Method ◽  
High Accuracy ◽  
Time Step ◽  
Volterra Type ◽  
Legendre Collocation Method

The purpose of this paper is to propose an efficient numerical method for solving Volterra-type integro-differential equation of the second kinds. This method based on Legendre-Gauss-Radau collocation, which is easy to be implemented especially for nonlinear and possesses high accuracy. Also, the method can be done by proceeding in time step by step. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique, and the results have been compared with the exact solution.

scholarly journals Analytic and numerical solution for duffing equations

2016 ◽  
Vol 5 (2) ◽  
pp. 115 ◽  
Author(s):  
Majeed AL-Jawary ◽  
Sayl Abd- AL- Razaq
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Duffing Equations ◽  
Linear And Nonlinear ◽  
New Iterative Method

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA<sup>®</sup> 9.0.</p>

scholarly journals Modified New Iterative Method for Solving Nonlinear Partial Differential Equations

2020 ◽  
Vol 19 ◽  
pp. 1-10
Author(s):  
Alaa K. Jabber
Keyword(s):  
Differential Equation ◽  
Differential Operator ◽  
Iterative Method ◽  
Initial Value Problems ◽  
Linear Differential Operator ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
The Laplace Transform ◽  
Linear Differential ◽  
New Iterative Method

In this paper, the iterative method, proposed by Gejji and Jafari in 2006, has been modified for solving nonlinear initial value problems. The Laplace transform was used in this modification to eliminate the linear differential operator in the differential equation. The convergence of the solution was discussed according to the modification proposed. To illustrate this modification some examples were presented.

scholarly journals Application of Iterative Method for Solving Higher Order Integro-Differential Equations

2019 ◽  
Vol 32 (2) ◽  
pp. 51 ◽  
Author(s):  
Samaher M. Yassein
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Numerical Methods ◽  
Differential Equations ◽  
Iterative Method ◽  
Convergent Series ◽  
Higher Order ◽  
Series Solutions ◽  
Solution Series ◽  
A New Technique

The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

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