Multi-adaptive time integration
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Nonlinear Krylov and moving nodes in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
On the stability and performance of discrete event methods for simulating continuous systems
Journal of Computational Physics
Algorithms and Data Structures for Multi-Adaptive Time-Stepping
ACM Transactions on Mathematical Software (TOMS)
Nonlinear Krylov and moving nodes in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
A Posteriori Error Analysis for the Use of Lookup Tables in Cardiac Electrophysiology Simulations
SIAM Journal on Scientific Computing
A Hybrid Implicit-Explicit Adaptive Multirate Numerical Scheme for Time-Dependent Equations
Journal of Scientific Computing
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has its own time-step sequence. This paper contains a description of the methods, an analysis of their basic properties, and a posteriori error analysis. In the accompanying paper [A. Logg, SIAM J. Sci. Comput., submitted], we present adaptive algorithms for time-stepping and global error control based on the results of the current paper.