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arXiv · 2508.13824

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

I. S. Popov
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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.

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I. S. Popov. 2026-04-14. Theory and internal structure of ADER-DG method for ordinary differential equations. https://doi.org/10.1137/25m1787008

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