In this paper we shall give practical and numerical solutions of the Laplace equation on multidimensional spaces and show their numerical experiments by using computers. Our method is based on the Dirichlet principle by combinations with generalized inverses, Tikhonov's regularization and the theory of reproducing kernels.
CITATION STYLE
Matsuura, T., & Saitoh, S. (2015). Dirichlet’s problem by using computers with the theory of reproducing kernels. In Trends in Mathematics (Vol. 2, pp. 561–568). Springer International Publishing. https://doi.org/10.1007/978-3-319-12577-0_62
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