TY - JOUR

T1 - New iterative method for solving linear and nonlinear hypersingular integral equations

AU - Boykov, I. V.

AU - Roudnev, V. A.

AU - Boykova, A. I.

AU - Baulina, O. A.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

KW - Hypersingular integral equations

KW - Lyapunov stability theory

KW - Modified Hopfield network

KW - Nonlinear algebraic equations

KW - NUMERICAL-SOLUTION

KW - CONVERGENCE

KW - APPROXIMATE SOLUTION

KW - ALGORITHMS

KW - FINITE-PART INTEGRALS

UR - http://www.scopus.com/inward/record.url?scp=85041485267&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2018.01.010

DO - 10.1016/j.apnum.2018.01.010

M3 - Article

AN - SCOPUS:85041485267

VL - 127

SP - 280

EP - 305

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -