Integral Operators Related to Boundary Value Problems in 2-D Domains with Cuts

2000 ◽  
pp. 707-718
Author(s):  
P. A. Krutiskii
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Integral Operators

The application of integral equation methods to the numerical solution of some exterior boundary-value problems

1971 ◽  
Vol 323 (1553) ◽  
pp. 201-210 ◽  
Keyword(s):  
Integral Equation ◽  
Wave Equation ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Integral Operators ◽  
Exterior Boundary ◽  
Integral Equation Methods ◽  
Singular Kernels ◽  
Single Integral

The application of integral equation methods to exterior boundary-value problems for Laplace’s equation and for the Helmholtz (or reduced wave) equation is discussed. In the latter case the straightforward formulation in terms of a single integral equation may give rise to difficulties of non-uniqueness; it is shown that uniqueness can be restored by deriving a second integral equation and suitably combining it with the first. Finally, an outline is given of methods for transforming the integral operators with strongly singular kernels which occur in the second equation.

scholarly journals Explicit characteristic equations for integral operators arising from well-posed boundary value problems of finite beam deflection on elastic foundation

2021 ◽  
Vol 6 (10) ◽  
pp. 10652-10678
Author(s):  
Sung Woo Choi ◽  
Keyword(s):  
Boundary Value Problems ◽  
Elastic Foundation ◽  
Boundary Value ◽  
Integral Operators ◽  
Beam Deflection ◽  
Diagonal Form ◽  
Point Boundary ◽  
Characteristic Equations ◽  
Block Diagonal Form ◽  
Well Posed

<abstract><p>Characteristic equations for the whole class of integral operators arising from arbitrary well-posed two-point boundary value problems of finite beam deflection resting on elastic foundation are obtained in terms of $ 4 \times 4 $ matrices in block-diagonal form with explicit $ 2 \times 2 $ blocks.</p></abstract>

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