ON THE ASYMPTOTIC BEHAVIOR, FOR LARGE VALUES OF THE TIME, OF SOLUTIONS OF EXTERIOR BOUNDARY VALUE PROBLEMS FOR THE WAVE EQUATION WITH TWO SPACE VARIABLES

1979 ◽  
Vol 35 (3) ◽  
pp. 377-423 ◽  
Author(s):  
L A Muraveĭ
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Exterior Boundary

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 The solution of some integral equations

1987 ◽  
Vol 29 (2) ◽  
pp. 203-215
Author(s):  
John F. Ahner ◽  
John S. Lowndes
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Laplace Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Fredholm Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Triple Integral Equations

AbstractAlgorithms are developed by means of which certain connected pairs of Fredholm integral equations of the first and second kinds can be converted into Fredholm integral equations of the second kind. The methods are then used to obtain the solutions of two different sets of triple integral equations tht occur in mixed boundary value problems involving Laplace' equation and the wave equation respectively.

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