A Novel Iterative Method Based on Bernstein-Adomian Polynomials to Solve Non-Linear Differential Equations

Yousif, Afaf Nasser; Qasim, Ahmed Farooq

doi:10.4236/oalib.1106267

Cited by 4 publications

(1 citation statement)

References 12 publications

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“…There are various new approximate analytical methods for solving differential equations. For example, in [1,2] investigated the use of an artificial neural network based on models for solving linear ordinary differential equations of the first and second order with a constant coefficient with initial conditions. To solve differential equations, non-standard difference schemes were proposed and developed in [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Engineering method for calculating fluid flow in pipes with different cross sections in energy and technological processes

Dalabaev

Hasanova

2023

E3S Web Conf.

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Section: Introductionmentioning

confidence: 99%

Engineering method for calculating fluid flow in pipes with different cross sections in energy and technological processes

Dalabaev

Hasanova

2023

E3S Web Conf.

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An Advantageous Numerical Method for Solution of Linear Differential Equations by Stancu Polynomials

Nese Isler

2024

Trends Comput Sci Inf Technol

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In this study, a numerical method that is alternative to the Bernstein collocation method has been investigated for solution of the linear differential equations. The theory of the method has been constituted by considering the Stancu polynomials and their algebric properties. The applicability of the method has been indicated on initial and boundary value problems. In addition, the numerical results of the proposed method have been compared with the numerical results of the known method had the best approximation in the past studies. Therefore, whether usability and efficiency of the proposed method is or not has been presented. 2020 Mathematics subject classification: 41A10, 65L05, 65L10 , 65L60

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The Approximation Error of Ordinary Differential Equations Based on the Moved Node Method

Dalabaev¹,

Hasanova²

2022

JAMP

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One of the central issues in solving differential equations by numerical methods is the issue of approximation. The standard way of approximating differential equations by numerical methods (particularly difference methods) is to question the degree of approximation in the form ( ) p O h . Here h is the grid step. In this case we have an implicit approximation. Based on the difference equation approximating the differential equation, the order of approximation is obtained using the Taylor series. However, it is possible to calculate the approximation error at nodal points based on the method of moving nodes. The method of moving nodes allows obtaining an approximate analytical expression. On the basis of the approximate form, it is possible to calculate the approximation error. The analytical form of the approximation makes it possible to efficiently calculate this error. On the other hand, the property of this error allows the construction of new improved circuits. In addition, based on these types of errors, you can create a differential analog of the difference equation that gives an exact approximation.

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A Novel Iterative Method Based on Bernstein-Adomian Polynomials to Solve Non-Linear Differential Equations

Cited by 4 publications

References 12 publications

Engineering method for calculating fluid flow in pipes with different cross sections in energy and technological processes

Engineering method for calculating fluid flow in pipes with different cross sections in energy and technological processes

An Advantageous Numerical Method for Solution of Linear Differential Equations by Stancu Polynomials

The Approximation Error of Ordinary Differential Equations Based on the Moved Node Method

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