Singular Linear Differential-Algebraic Equations with Constant Coefficients Necessarily Admit Non-Computable Solutions

Holger Boche; Volker Pohl; H. Vincent Poor; Frank H. P. Fitzek

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arXiv · 2610.28188

Singular Linear Differential-Algebraic Equations with Constant Coefficients Necessarily Admit Non-Computable Solutions

Holger Boche·Volker Pohl·H. Vincent Poor·Frank H. P. Fitzek

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Abstract

If a regular linear differential-algebraic equation has a unique solution, this solution is known to be Turing computable. In contrast, this paper shows that singular linear differential-algebraic equations exhibit fundamentally different computability properties. More precisely, we show that for every linear differential-algebraic equation (LDAE) with constant computable coefficients, there exists a computable input function with strong regularity properties such that the LDAE admits a unique solution, yet this solution is not Turing computable. In fact, the solution is non-computable at certain computable times.

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BibTeX RIS

Holger Boche, Volker Pohl, H. Vincent Poor, Frank H. P. Fitzek. 2026-10-20. Singular Linear Differential-Algebraic Equations with Constant Coefficients Necessarily Admit Non-Computable Solutions. https://arxiv.org/abs/2610.28188

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