Explicit Runge approximation for the Helmholtz equation in ℝ 2
Abstract The main theme of this paper is to study Runge approximation for the Helmholtz equation in ℝ 2 {\mathbb{R}^{2}} in an explicit and numerically implementable way, using Fourier series, for both interior and exterior boundary value problems. Compared with existing qualitative Runge approximation results, the main advantage of our approach is its numerical implementability. Our numerical implementation is supported by explicit quantitative estimates.
Authors
- Tingyue Li (ORCID: https://orcid.org/0009-0000-4045-9244)
- Yu Chen (ORCID: https://orcid.org/0000-0003-3864-8446)
- Jin Cheng
Institutions
- Shanghai University of Finance and Economics (CN)
- Fudan University (CN)
Publication Details
- Journal
- Journal of Inverse and Ill-Posed Problems
- Published
- 2026-10-26
- DOI
- https://doi.org/10.1515/jiip-2026-0086
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- National Key Research and Development Program of China
- Fundamental Research Funds for the Central Universities