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 3 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.

View full text Add to dashboard Cite

show abstract

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.

View full text Add to dashboard Cite

show abstract

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

Dalabaev¹,

Hasanova²

2022

JAMP

View full text Add to dashboard Cite

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.

show abstract

The Study of Root Subspace Decomposition between Characteristic Polynomials and Minimum Polynomial

Kang,

Wang,

Liu

2024

OJAppS

View full text Add to dashboard Cite

Let  be the linear transformation on the linear space V in the field P, i V λ be the root subspace corresponding to the characteristic polynomial of the eigenvalue i λ , and i W λ be the root subspace corresponding to the minimum polynomial of i λ . Consider the problem of whether i V λ and i W λ are equal under the condition that the characteristic polynomial of  has the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove thatCompared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng's book "Introduction to Differential Geometry."

show abstract

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

Cited by 3 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

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

The Study of Root Subspace Decomposition between Characteristic Polynomials and Minimum Polynomial

Contact Info

Product

Resources

About