Journal of Computational and Applied Mathematics
Two polynomial methods of calculating functions of symmetric matrices
USSR Computational Mathematics and Mathematical Physics
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Calculation of functions of unsymmetric matrices using Arnoldi's method
Computational Mathematics and Mathematical Physics
Fourier analysis of numerical algorithms for the Maxwell equations
Journal of Computational Physics
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
SIAM Journal on Matrix Analysis and Applications
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
The Gautschi time stepping scheme for edge finite element discretizations of the Maxwell equations
Journal of Computational Physics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Weighted sequential splittings and their analysis
Computers & Mathematics with Applications
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Motivated by numerical solution of the time-dependent Maxwell equations, we consider splitting methods for a linear system of differential equations w^'(t)=Aw(t)+f(t), A@?R^n^x^n split into two subproblems w"1^'(t)=A"1w"1(t)+f"1(t) and w"2^'(t)=A"2w"2(t)+f"2(t), A=A"1+A"2, f=f"1+f"2. First, expressions for the leading term of the local error are derived for the Strang-Marchuk and the symmetrically weighted sequential splitting methods. The analysis, done in assumption that the subproblems are solved exactly, confirms the expected second order global accuracy of both schemes. Second, several relevant numerical tests are performed for the Maxwell equations discretized in space either by finite differences or by finite elements. An interesting case is the splitting into the subproblems w"1^'=Aw"1 and w"2^'=f (with the split-off source term f). For the central finite difference staggered discretization, we consider second order splitting schemes and compare them to the classical Yee scheme on a test problem with loss and source terms. For the vector Nedelec finite element discretizations, we test the Gautschi-Krylov time integration scheme. Applied in combination with the split-off source term, it leads to splitting schemes that are exact per split step. Thus, the time integration error of the schemes consists solely of the splitting error.