Theory and internal structure of ADER-DG method for ordinary differential equations

I. S. Popov

Theory and internal structure of ADER-DG method for ordinary differential equations

Numerical Analysis 2026-04-15 v2 Numerical Analysis Spectral Theory Applied Physics Computational Physics

Authors: I. S. Popov

Abstract

Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is $A$ - and $AN$ -stable, $L$ -stable, $B$ - and $BN$ -stable, and algebraically stable. Several other relations useful for an application and implementation of the ADER-DG method are proved. Applications of the ADER-DG method demonstrated compliance with the expected theoretical results.

Keywords

ADER-DG ordinary differential equations stability convergence approximation

Cite

@article{arxiv.2508.13824,
  title  = {Theory and internal structure of ADER-DG method for ordinary differential equations},
  author = {I. S. Popov},
  journal= {arXiv preprint arXiv:2508.13824},
  year   = {2026}
}

Comments

20 pages, 7 figures, 2 tables

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