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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):281-286; doi:10.1093/qjmam/1.1.281
© 1948 by Oxford University Press
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THE COMBINED USE OF RELAXATION METHODS AND FOURIER TRANSFORMS IN THE SOLUTION OF SOME THREE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

C. J. TRANTER

( Military College of Science Shrivenham )

A method is proposed whereby, using Fourier transforms, some three-dimensional boundary value problems are brought within the scope of normal relaxation methods. The method is illustrated by the solution of Poisson's equation inside the region bounded by a right cylinder of any cross-section when values of the unknown function are given on the curved surface and when either (i) values of the function or (ii) values of its normal gradient are specified over the flat ends. The steady temperature inside a cube when the surface temperature is constant on one face and zero on the remaining faces is worked out as a detailed example. The solution is also sketched in the case of very long cylinders when only one end affects the required function.


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