{
  "abstract": "ADER-DG numerical method with the LST-DG predictor, when used to solve hyperbolic equations with stiff source terms, exhibits properties characteristic of IMEX computational schemes. With increasing stiffness, characterized by the parameter $z = ν{Δt}^{n} < 0$, the maximum of the Courant number $\\mathrm{CFL}_{\\rm max}$ of the ADER-DG numerical method increases. In the region of strong stiffness $|z| \\gg 1$, a linear increase in the Courant number $\\mathrm{CFL}_{\\rm max}(z) \\sim |z|$ occurs. In the region of small source terms $|z| \\ll 1$, the results $\\mathrm{CFL}_{\\rm max}(z)$ transform into known results for the problem $\\mathrm{CFL}_{\\rm max}(0)$ without source terms. In the transition region $|z| \\sim 1$, a range of insignificant decrease in the Courant number $\\mathrm{CFL}_{\\rm max}(z)$ is discovered. In the linear case, instability is violated precisely when one of the matrix eigenvalues reaches $λ= -1$, regardless of the phase $θ$ of the numerical solution. A rigorous stability theory of the ADER-DG numerical method for stiff problems for arbitrary degree $N$ of basis polynomials is constructed. The stability condition is simplified to solving a polynomial equation for the Courant number $\\mathrm{CFL}$. Highly accurate dependencies of the Courant number $\\mathrm{CFL}_{\\rm max}(N, z)$ of the ADER-DG method on the parameter $z$ are obtained. A rigorous direct proof of the approximation of the ADER-DG method is presented. Approximation orders $p = N+1$ for arbitrary degrees $N$ are rigorously derived. A set of numerical experiments is carried out to apply the ADER-DG method to solving both a linear advection-reaction equation and the system of Euler equations for a two-component reacting medium. The results obtained in these calculations confirm the theoretical results well.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30852",
  "author_total": 2,
  "authors": [
    {
      "name": "I. S. Popov"
    },
    {
      "name": "A. P. Popova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8at654wf36byg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30852",
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  "id": "8at654wf36byg",
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  "landing_url": "https://arxiv.org/abs/2610.30852",
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      "2206|Computational Fluid Dynamics and Aerodynamics"
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  "openalex": "W7223359261",
  "pdf_url": "https://arxiv.org/pdf/2610.30852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8at654wf36byg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.30852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.app-ph",
      "subfield": "applied-instrumentation"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Stiff source terms inside ADER-DG method",
  "title_text": "Stiff source terms inside ADER-DG method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/8at654wf36byg",
  "venue": "arXiv",
  "versions": []
}