Journal of Computational and Applied Mathematics
A method for exponential propagation of large systems of stiff nonlinear differential equations
Journal of Scientific Computing
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
An exponential method of numerical integration of ordinary differential equations
Communications of the ACM
Exponential time differencing for stiff systems
Journal of Computational Physics
Commutator-free Lie group methods
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
B-series and Order Conditions for Exponential Integrators
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Exponential Rosenbrock-Type Methods
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
Journal of Computational and Applied Mathematics
Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
We propose a new class of the exponential propagation iterative methods of Runge-Kutta-type (EPIRK). The EPIRK schemes are exponential integrators that can be competitive with explicit and implicit methods for integration of large stiff systems of ODEs. Introducing the new, more general than previously proposed, ansatz for EPIRK schemes allows for more flexibility in deriving computationally efficient high-order integrators. Recent extension of the theory of B-series to exponential integrators [1] is used to derive classical order conditions for schemes up to order five. An algorithm to systematically solve these conditions is presented and several new fifth order schemes are constructed. Several numerical examples are used to verify the order of the methods and to illustrate the performance of the new schemes.