Work

Explicit Runge approximation for the Helmholtz equation in ℝ 2

Year: 2026

Type: article

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.

Source: Journal of Inverse and Ill-Posed Problems

DOI: 10.1515/jiip-2026-0086

Authors: Yu Chen, Jin Cheng, Tingyue Li

Institutions: Shanghai University of Finance and Economics, Fudan University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712