most citedSummation-by-parts approximations of the second derivative: Pseudoinverses of singular operators and revisiting the sixth order accurate narrow-stencil operator

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math.NA2024

Inverting the sum of two singular matrices

Sofia Eriksson, Jonas Nordqvist

Square matrices of the form are considered. An explicit expression for the inverse is given, provided $\widetilde{\m…

math.NA2020★ 1 cited

Summation-by-parts approximations of the second derivative: Pseudoinverses of singular operators and revisiting the sixth order accurate narrow-stencil operator

Sofia Eriksson, Siyang Wang

We consider finite difference approximations of the second derivative, exemplified in Poisson's equation, the heat equation and the wave equation. The finite difference operators s…

math.NA2020

Inverses of SBP-SAT finite difference operators approximating the first and second derivative

Sofia Eriksson

The scalar, one-dimensional advection equation and heat equation are considered. These equations are discretized in space, using a finite difference method satisfying summation-by-…