A Diffeomorphic Variable-Step Finite Difference Method

Autor:	Amaro, Mário B.
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Physics - Computational Physics
Druh dokumentu:	Working Paper
Popis:	This work introduces an approach to variable-step Finite Difference Method (FDM) where non-uniform meshes are generated via a weight function, which establishes a diffeomorphism between uniformly spaced computational coordinates and variably spaced physical coordinates. We then derive finite difference approximations for derivatives on variable meshes in both one-dimensional and multi-dimensional cases, and discuss constraints on the weight function. To demonstrate efficacy, we apply the method to the two-dimensional time-independent Schr\"odinger equation for a harmonic oscillator, achieving improved eigenfunction resolution without increased computational cost. Comment: 6 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.05598 Zobrazit plný text záznamu View this record from Arxiv