Add to ORKGThis paper discusses an efficient implementation of the generation of order conditions for the construction of exponential integrators like exponential splitting and Magnus-type methods in the computer algebra system Maple. At the core of this implementation is a new algorithm for the computation of coefficients of words in the formal expansion of the local error of the integrator. The underlying theoretical background including an analysis of the structure of the local error is briefly reviewed. As an application the coefficients of all 8th order self-adjoint commutator-free Magnus-type integrators involving the minimum number of 8 exponentials are computed
Modular algorithms for linear equations solution, matrix inversion, determinant calculation, null sp...
Approximate resolution of linear systems of differential equations with varying coefficients is a re...
AbstractWe explore reliability, stability and accuracy of determining the polynomials which define t...
Abstract. A new algorithm is developed for computing etAB, where A is an n × n matrix and B is n×n0 ...
A new algorithm is developed for computing $e^{tA}B$, where $A$ is an $n\times n$ matrix and $B$ is ...
A new algorithm is developed for computing $e^{tA}B$, where $A$ is an $n\times n$ matrix and $B$ is ...
We discuss the structure of the local error of exponential operator splitting methods. In particular...
A new algorithm for computing integrals involving the matrix exponential is given. The method emplo...
This PhD-thesis contains an introduction and six research papers sorted chronologically, of which th...
Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration...
We introduce a general format of numerical ODE-solvers which include many of the recently proposed e...
This paper takes a look at numerical procedures for computing approximation of the exponential of a ...
The computer algebra system Maple contains a basic set of commands for working with Lie algebras. Th...
The class of commutator-free quasi-Magnus (CFQM) exponential integrators provides a favourable alter...
We consider the numerical integration of high-order linear non-homogeneous differential equations, w...
Modular algorithms for linear equations solution, matrix inversion, determinant calculation, null sp...
Approximate resolution of linear systems of differential equations with varying coefficients is a re...
AbstractWe explore reliability, stability and accuracy of determining the polynomials which define t...
Abstract. A new algorithm is developed for computing etAB, where A is an n × n matrix and B is n×n0 ...
A new algorithm is developed for computing $e^{tA}B$, where $A$ is an $n\times n$ matrix and $B$ is ...
A new algorithm is developed for computing $e^{tA}B$, where $A$ is an $n\times n$ matrix and $B$ is ...
We discuss the structure of the local error of exponential operator splitting methods. In particular...
A new algorithm for computing integrals involving the matrix exponential is given. The method emplo...
This PhD-thesis contains an introduction and six research papers sorted chronologically, of which th...
Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration...
We introduce a general format of numerical ODE-solvers which include many of the recently proposed e...
This paper takes a look at numerical procedures for computing approximation of the exponential of a ...
The computer algebra system Maple contains a basic set of commands for working with Lie algebras. Th...
The class of commutator-free quasi-Magnus (CFQM) exponential integrators provides a favourable alter...
We consider the numerical integration of high-order linear non-homogeneous differential equations, w...
Modular algorithms for linear equations solution, matrix inversion, determinant calculation, null sp...
Approximate resolution of linear systems of differential equations with varying coefficients is a re...
AbstractWe explore reliability, stability and accuracy of determining the polynomials which define t...