Two different approaches for transforming domain integrals to the boundary
The author describes in rather general terms methods for solving boundary value problems involving the Laplacian. The first is the so called `dual reciprocity' method, and consists of approximating the unknown function by a linear combination of known solutions of the given equation followed by the use of Green's third formula. There is some discussion on the choice of appropriate functions, which for the Laplacian are multiples of \(r^ 3\) where r is the distance from an arbitrary point to fixed points in the domain. There is a brief discussion of axisymmetric problems. The second method is the `multiple reciprocity method' in which another set of approximating functions defined by a recurrence relation is used, and is again based on particular solutions. This is illustrated with an application to a problem involving Poisson's equation. The author states that the methods give accurate results on test examples. There are four numerical examples in which the results are given graphically and compared with known solutions. Numerous references are given to the work of the author and his co-workers.
scientific article; zbMATH DE number 4213368
scientific article