2024
DOI: 10.1093/imanum/drae032
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Computing Klein-Gordon Spectra

Frank Rösler,
Christiane Tretter

Abstract: We study the computational complexity of the eigenvalue problem for the Klein–Gordon equation in the framework of the Solvability Complexity Index Hierarchy. We prove that the eigenvalue of the Klein–Gordon equation with linearly decaying potential can be computed in a single limit with guaranteed error bounds from above. The proof is constructive, i.e. we obtain a numerical algorithm that can be implemented on a computer. Moreover, we prove abstract enclosures for the point spectrum of the Klein–Gordon equati… Show more

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