Theory and Internal Structure of ADER-DG Method for Ordinary Differential Equations
Abstract
Abstract. Investigation of the approximation properties, convergence, and stability of the Arbitrary higher-order DERivatives discontinuous Galerkin (ADER-DG) method for solving an ODE system is carried out. The ADER-DG method is [Formula: see text]- and [Formula: see text]-stable, [Formula: see text]-stable, [Formula: see text]- and [Formula: see text]-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.
Fields of Study & Subjects
Electromagnetic Simulation and Numerical Methods
Advanced Numerical Methods in Computational Mathematics
Magnetic Properties and Applications
Publication details
- Journal / source
- SIAM Journal on Numerical Analysis
- Volume
- 64
- Issue
- 4
- Pages
- 1561–1581
- Publication date
- 6 August 2026
- Language
- EN