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 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 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.

scholarly journals Solving Kuramoto–Sivashinsky equation by the new iterative method and estimate the optimal parameters by using PSO algorithm

2020 ◽  
Vol 19 (2) ◽  
pp. 709 ◽  
Author(s):  
Karam Adel Abed
Keyword(s):  
Particle Swarm Optimization ◽  
Fitness Function ◽  
Approximate Solutions ◽  
Pso Algorithm ◽  
High Accuracy ◽  
Parameters Estimation ◽  
Optimal Parameters ◽  
Swarm Optimization ◽  
Sivashinsky Equation ◽  
New Iterative Method

<p>In this study, optimal parameters estimation is performed for non-linear (Kuramoto-Sivashinsky) equation using a crossbred method between Particle swarm optimization (PSO) algorithm and (NIM) technique and for the appropriateness we call it (PSO-NIM). It turns out that the optimal parameters significantly improve the solutions when we use a fitness function suitable for the issue. The results confirmed that the get approximate solutions are in suitable pact with the exact solutions and the proposed method provides high accuracy and efficiency in comparison with (NIM) which use traditionally chosen parameters.</p>

scholarly journals Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Samaher Marez
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Iterative Process ◽  
Initial Conditions ◽  
High Accuracy ◽  
Series Solutions ◽  
Math Program ◽  
The Right

  The aim of this paper, a reliable iterative method is presented for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method.  Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibit that this technique has compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

scholarly journals A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Numerical Analysis ◽  
Iterative Method ◽  
Iterative Algorithm ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Numerical Continuation ◽  
Stationary Type ◽  
Continuation Technique ◽  
New Iterative Method

The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.

scholarly journals The Laplace-Adomian-Pade Technique for the ENSO Model

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yi Zeng
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
High Accuracy ◽  
Padé Method

The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.

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 Iterative Solutions of Hirota Satsuma Coupled KDV and Modified Coupled KDV Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Muhammad Jibran ◽  
Rashid Nawaz ◽  
Asfandyar Khan ◽  
Sajjad Afzal
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Kdv Equations ◽  
Homotopy Analysis ◽  
Iterative Solutions ◽  
Coupled Kdv Equations ◽  
New Iterative Method

In this article the approximate solutions of nonlinear Hirota Satsuma coupled Korteweg De- Vries (KDV) and modified coupled KDV equations have been obtained by using reliable algorithm of New Iterative Method (NIM). The results obtained give higher accuracy than that of homotopy analysis method (HAM). The obtained solutions show that NIM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

scholarly journals Approximate Solutions for Systems of Volterra Integro-differential Equations Using Laplace –Adomian Method

2020 ◽  
pp. 2655-2662
Author(s):  
Firas S. Ahmed
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Adomian Decomposition ◽  
Adomian Method ◽  
The Given

Some modified techniques are used in this article in order to have approximate solutions for systems of Volterra integro-differential equations. The suggested techniques are the so called Laplace-Adomian decomposition method and Laplace iterative method. The proposed methods are robust and accurate as can be seen from the given illustrative examples and from the comparison that are made with the exact solution.

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