New iterative method for solving linear and nonlinear hypersingular integral equations

We propose a method for solving linear and nonlinear hypersingular integral equations. For nonlinear equations the advantage of the method is in rather weak requirements for the nonlinear operator behavior in the vicinity of the solution. The singularity of the kernel not only guarantees strong diag...

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Bibliographic Details
Published in:Applied numerical mathematics 2018-05, Vol.127, p.280-305
Main Authors: Boykov, I.V., Roudnev, V.A., Boykova, A.I., Baulina, O.A.
Format: Article
Language:English
Subjects:
Hypersingular integral equations
Lyapunov stability theory
Modified Hopfield network
Nonlinear algebraic equations
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Summary:We propose a method for solving linear and nonlinear hypersingular integral equations. For nonlinear equations the advantage of the method is in rather weak requirements for the nonlinear operator behavior in the vicinity of the solution. The singularity of the kernel not only guarantees strong diagonal dominance of the discretized equations, but also guarantees the convergence of a simple iterative scheme based on Lyapunov stability theory. The resulting computational method can be implemented with recurrent neural networks or analog computers.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2018.01.010