An iterative method for solving elliptic BVP in one-dimension
Analysis of PDEs
2024-10-10 v1 Numerical Analysis
Numerical Analysis
Abstract
This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally superior to the original formulation as less computations are required to obtain an approximation of the same accuracy. Convergence of the method is justified and supported by some theoretical results. We show that for a sufficiently smooth forcing data, the method always converge for a relatively small truncation order. The method is tested using some problems with exact solutions.
Cite
@article{arxiv.2410.06276,
title = {An iterative method for solving elliptic BVP in one-dimension},
author = {Christian O. Bernal Zelaya and Prosper Torsu},
journal= {arXiv preprint arXiv:2410.06276},
year = {2024}
}
Comments
11 pages