The main theme of this paper is to study Runge approximation for the Helmholtz equation in ℝ 2 {R²} 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.
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Chen et al. (2026) studied this question.
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