Order conditions for exponential integrators
Provides a systematic tool for designing efficient exponential integrators, benefiting numerical analysts solving evolution equations.
This paper develops an algebraic framework for generating order conditions for exponential integrators, enabling the construction of high-order methods. Using this framework, a new 8th order commutator-free Magnus-type integrator requiring only 8 exponentials is derived.
This paper provides an algebraic framework for the generation of order conditions for the construction of exponential integrators like splitting and Magnus-type methods for the numerical solution of evolution equations. The generation of order conditions is based on an analysis of the structure of the leading local error term of such an integrator, and on a new algorithm for the computation of coefficients of words in expressions involving exponentials. As an application a new 8th order commutator-free Magnus-type integrator involving only 8 exponentials is derived.