Multi-Adaptive Galerkin Methods for ODEs II: Implementation and Applications

TL;DR

This paper discusses the implementation and application of multi-adaptive Galerkin methods for solving ordinary differential equations, focusing on adaptive algorithms, solution techniques, and demonstrating their effectiveness on complex systems.

Contribution

It introduces adaptive algorithms and implementation features for multi-adaptive Galerkin methods, extending previous work with practical computational strategies and diverse applications.

Findings

Effective error control algorithms developed

Successful application to Lorenz system and solar system

Demonstrated efficiency on time-dependent PDEs

Abstract

Continuing the discussion of the multi-adaptive Galerkin methods mcG(q) and mdG(q) presented in [A. Logg, SIAM J. Sci. Comput., 24 (2003), pp. 1879-1902], we present adaptive algorithms for global error control, iterative solution methods for the discrete equations, features of the implementation Tanganyika, and computational results for a variety of ODEs. Examples include the Lorenz system, the solar system, and a number of time-dependent PDEs.