Numerical solution of Boundary-Value problems by the method of integral operators

1965 ◽  
Vol 7 (1) ◽  
pp. 42-65 ◽  
Author(s):  
Stefan Bergman ◽  
John G. Herriot
Keyword(s):  
Numerical Solution ◽  
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.

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