On the fundamental solutions-based inversion of Laplace matrices
F.J. Vermolen (TU Delft - Numerical Analysis, University of Hasselt)
D.R. Bakker (Student TU Delft)
Kees Vuik (TU Delft - Delft Institute of Applied Mathematics)
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Abstract
The discretisation of the Laplacian results into the well-known Laplace matrix. In the case of a one dimensional problem, an explicit formula for its inverse is derived on the basis of fundamental solutions (Green’s functions) for general boundary conditions. For a linear reaction–diffusion equation, approximations of the inverse are given.
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