Construction of one-frequency solutions of boundary-value problems for a nonautonomous wave equation

1994 ◽  
Vol 46 (9) ◽  
pp. 1404-1409 ◽  
Author(s):  
B. I. Sokil
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Boundary Value

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.

XII.—Paraboloidal Co-ordinates and Laplace's Equation

1963 ◽  
Vol 66 (3) ◽  
pp. 129-139
Author(s):  
F. M. Arscott
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Subsequent Paper ◽  
Laplace’S Equation ◽  
Mathieu Functions ◽  
Laplace's Equation ◽  
Normal Surfaces ◽  
Special Cases ◽  
Hyperbolic Paraboloids

SynopsisIn this paper we examine the general paraboloidal co-ordinate system, in which the normal surfaces are elliptic or hyperbolic paraboloids, including as special cases the “parabolic plate” and the “plate with a parabolic hole”. We then show that normal solutions of Laplace's equation in these co-ordinates are given as products of three Mathieu functions, and apply this to the solution of boundary-value problems for Laplace's equation in these co-ordinates. In a subsequent paper the corresponding treatment of the wave equation will be given.

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