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

I. S. Popov

doi:10.1137/25M1787008

paper

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

arXiv:2508.13824 · doi:10.1137/25M1787008

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 $A N$ -stable, $L$ -stable, $B$ - and $B N$ -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.

20 pages, 7 figures, 2 tables