Research output: Contribution to journal › Article › peer-review
New iterative method for solving linear and nonlinear hypersingular integral equations. / Boykov, I. V.; Roudnev, V. A.; Boykova, A. I.; Baulina, O. A.
In: Applied Numerical Mathematics, Vol. 127, 01.05.2018, p. 280-305.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 37232832