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- W1502714783 abstract "A procedure has recently been discovered by which the classical separation of variables method can be extended to solve linear boundary value problems for complex geometries. In brief, the procedure consists of embedding the given complex geometry in a larger domain on which complete sets of eigenfunctions exist The latter are then used to represent the field in the given complex geometry. Since the eigenfunctions are not in general orthogonal on the given boundary, the unknown coefficients are evaluated by a least squares procedure. The details in a specific example, that of two-dimensional heat conduction in a solid of complex shape, are given so that the method can be easily understood and applied. In this case the field satisfies Laplace's equation with given data on the boundary. Since the method is simple and easy to apply, it provides an efficient, extremely accurate and elegant alternative to brute force computation. It is hoped that the method will be taught to college and university students who should have no difficulty in grasping it." @default.
- W1502714783 created "2016-06-24" @default.
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- W1502714783 date "2005-01-01" @default.
- W1502714783 modified "2023-09-23" @default.
- W1502714783 title "A new separation of variables method for complex geometries" @default.
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