New iterative method for solving linear and nonlinear hypersingular integral equations

Roudnev, Vladimir; Boykova, Alla; Baulina, O. A.

doi:10.1016/j.apnum.2018.01.010

Cited by 13 publications

(4 citation statements)

References 10 publications

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“…It is also stable to the perturbation of the coefficients and right-hand sides of Equation (20). The proof of this statement and the corresponding theorems can be found in [38].…”

Section: Approximate Solution Of Systems Of Algebraic Equations On Ho...mentioning

confidence: 93%

“…The system of Equation ( 35) can be solved by any numerical method. Examples of solving linear hypersingular integral equations by the continuous operator method are given in [38].…”

Section: Max Maxmentioning

confidence: 99%

“…We noted above that the continuous operator method has been applied for solving inverse coefficients problems [49], hypersingular integral equations [38], and inverse problems in astrophysics [50]. In each of these works, the obtained results were compared with the known ones.…”

Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

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Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Roudnev

Boykova

2022

Mathematics

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A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate solution of the Fredholm integral equation, and linear and nonlinear singular and hypersingular integral equations, using a continuous method for solving operator equations. This method assumes that the original system is associated with a Cauchy problem for systems of ordinary differential equations on Hopfield neural networks. We present sufficient conditions for the Hopfield networks’ stability defined via coefficients of systems of differential equations.

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“…It is also stable to the perturbation of the coefficients and right-hand sides of Equation (20). The proof of this statement and the corresponding theorems can be found in [38].…”

Section: Approximate Solution Of Systems Of Algebraic Equations On Ho...mentioning

confidence: 93%

“…The system of Equation ( 35) can be solved by any numerical method. Examples of solving linear hypersingular integral equations by the continuous operator method are given in [38].…”

Section: Max Maxmentioning

confidence: 99%

See 1 more Smart Citation

Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Roudnev

Boykova

2022

Mathematics

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“…In [21] - [26] a collocation and spline-collocation methods for solving hypersingular and polyhypersingular integral equations with even singularity has been developed and justified, and the nonlinear case is described in [24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Analytical Methods of Solving Hypersingular Integral Equations

Boykova¹

2017

UVP

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We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential equations. Well known that many types of differential equations can be solved in quadratures. So, we can receive analytical solutions for many types of linear and nonlinear hypersingular and polyhypersingular integral equations.

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Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study

Obaiys

Ibrahim

Ahmad

2019

Differential and Integral Inequalities

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New iterative method for solving linear and nonlinear hypersingular integral equations

Cited by 13 publications

References 10 publications

Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks

Analytical Methods of Solving Hypersingular Integral Equations

Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study

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