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ijs-3201
Efficient Modification of the Decomposition Method for Solving a System of PDEs
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     This paper presents an analysis solution for systems of partial differential equations using a new modification of the decomposition method to overcome the computational difficulties. Convergence of series solution was discussed with two illustrated examples, and the method showed a high-precision, being a fast approach to solve the non-linear system of PDEs with initial conditions. There is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials. The method does not require any discretization or assumption for a small parameter to be present in the problem. The steps of the suggested method are easily implemented, with high accuracy and rapid convergence to the exact solution, compared with other methods that can be used to solve systems of PDEs.

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Publication Date
Tue Jun 20 2023
Journal Name
Baghdad Science Journal
Numerical Solutions for the Nonlinear PDEs of Fractional Order by Using a New Double Integral Transform with Variational Iteration Method
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This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

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Publication Date
Fri Jul 19 2024
Journal Name
An International Journal Of Optimization And Control: Theories & Applications (ijocta)
Design optimal neural network based on new LM training algorithm for solving 3D - PDEs
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In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

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Publication Date
Mon Aug 14 2017
Journal Name
International Journal Of Intelligent Computing And Cybernetics
Two efficient methods for solving Schlömilch’s integral equation
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Purpose

In this paper, the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods. The Schlömilch’s integral equations have many applications in atmospheric, terrestrial physics and ionospheric problems. They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations. The paper aims to discuss these issues.

Design/methodology/approach

First, the authors apply a regularization meth

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Publication Date
Thu May 30 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Laplace transform-adomian decomposition approach for solving random partial differential equations
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Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.

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Publication Date
Wed Feb 08 2023
Journal Name
Iraqi Journal Of Science
Efficient Method for Color Iris Localization
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Iris detection is considered as challenging image processing task. In this study efficient method was suggested to detect iris and recognition it. This method depending on seed filling algorithm and circular area detection, where the color image converted to gray image, and then the gray image is converted to binary image. The seed filling is applied of the binary image and the position of detected object binary region (ROI) is localized in term of it is center coordinates are radii (i.e., the inner and out radius). To find the localization efficiency of suggested method has been used the coefficient of variation (CV) for radius iris for evaluation. The test results indicated that is suggested method is good for the iris detection.

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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
Sat Dec 01 2018
Journal Name
Ain Shams Engineering Journal
A semi-analytical iterative method for solving differential algebraic equations
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Publication Date
Thu Dec 30 2021
Journal Name
Iraqi Journal Of Science
A Reliable Iterative Transform Method for Solving an Epidemic Model
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    The main purpose of the work is to apply a new method, so-called LTAM, which couples the Tamimi and Ansari iterative method (TAM) with the Laplace transform (LT). This method involves solving a problem of non-fatal disease spread in a society that is assumed to have a fixed size during the epidemic period. We apply the method to give an approximate analytic solution to the nonlinear system of the intended model. Moreover, the absolute error resulting from the numerical solutions and the ten iterations of LTAM approximations of the epidemic model, along with the maximum error remainder, were calculated by using MATHEMATICA® 11.3 program to illustrate the effectiveness of the method.

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Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
New Iterative Method for Solving Nonlinear Equations
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The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

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Publication Date
Sun Jun 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Analytic Solutions For Integro-Differential Inequalities Using Modified Adomian Decomposition Method
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   This paper applies the Modified Adomian Decomposition Method (MADM) for solving Integro-Differential Inequality, this method  is one of effective to construct analytic approximate solutions for linear and nonlinear integro-differential inequalities without solving many integrals and transformed or discretization. Several examples are presented, the analytic results show that this method is a promising and powerful for solving these problems.

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