Wavelet based solutions to the Poisson and the Helmholtz equations on the n-dimensional unit sphere

2025/07/04 by Iglewska-Nowak, Ilona, Stefaniak, Piotr · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.03451

Abstract

We present a method of solving partial differential equations on the n-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the Poisson equation and to the Helmholtz equations. For the first one and for some special values of the parameter in the latter one, we derive a closed formula for the generalized Green function.

Citations

• Wavelet-based Methods for Numerical Solutions of Differential Equations
• A continuous spherical wavelet transform for~\mathcal C(\mathcal Sⁿ)

Cited by

• Green function to the biharmonic equation on n-dimensional sphere
• On the Green function to the Poisson and the Helmholtz equations on the n-dimensional unit sphere

Related

• Wavelet methods in partial differential equations on spheres
• On the Green function to the Poisson and the Helmholtz equations on the n-dimensional unit sphere
• A continuous spherical wavelet transform for~\mathcal C(\mathcal Sⁿ)
• Beyond Wavelets: Exactness theorems and algorithms for physical calculations
• Wavelet-based Methods for Numerical Solutions of Differential Equations