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The Nyström method for solving a class of singular integral equations and applications in 3D‐plate elasticity
Author(s) -
Kirsch Andreas,
Ritter Stefan
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990125)22:2<177::aid-mma36>3.0.co;2-f
Subject(s) - mathematics , singular integral , mathematical analysis , sobolev space , integral equation , nyström method , fredholm integral equation , collocation method , uniqueness , singular solution , boundary value problem , dirichlet problem , dirichlet integral , dirichlet's principle , ordinary differential equation , differential equation
The paper consists of two parts. In the first part we investigate a Nyström‐ or product integration method for second kind singular integral equations. We prove an asymptotically optimal error estimate in the scale of Sobolev Hilbert spaces. Although the result can also be obtained as a special case of a discrete iterated collocation method our proof is more direct and uses the Nyström interpolation. In the second part of this paper we consider the Dirichlet problem for thin elastic plates with transverse shear deformation. The boundary value problem is transformed into a 3 × 3 system of singular Fredholm integral equations of second kind. After discussing existence and uniqueness of the solution to the integral equations in a Sobolev space setting, we apply the Nyström method to solve the integral equations numerically. Copyright © 1999 John Wiley & Sons, Ltd.