Wavelet methods in partial differential equations on spheres

TL;DR

This paper introduces a wavelet-based approach for solving partial differential equations on n-dimensional spheres, utilizing continuous wavelet transforms derived from approximate identities to improve solution methods.

Contribution

It presents a novel wavelet method specifically designed for PDEs on spheres, expanding the toolkit for spherical PDE analysis.

Findings

Effective wavelet-based solution technique for spherical PDEs

Enhanced accuracy using continuous wavelet transforms

Potential for broader applications in spherical data analysis

Abstract

We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.