On the fundamental solutions-based inversion of Laplace matrices

Journal article (2022)

Authors

F.J. Vermolen Numerical Analysis - EEMCS , University of Hasselt
D.R. Bakker Student
Cornelis Vuik Delft Institute of Applied Mathematics
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2022 F.J. Vermolen, D.R. Bakker, Cornelis Vuik
DOI: https://doi.org/10.1016/j.rinam.2022.100288
More Info
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.