Cost-reduction implicit exponential Runge-Kutta methods for highly oscillatory systems

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Cites Work

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Exponentially fitted third derivative three-step methods for numerical integration of stiff initial value problems
Long time behavior of solutions of gKdV equations
ERKN integrators for systems of oscillatory second-order differential equations
Extended RKN-type methods with minimal dispersion error for perturbed oscillators
Generalized integrating factor methods for stiff PDEs
Symmetric exponential integrators with an application to the cubic Schrödinger equation
Runge-Kutta schemes for Hamiltonian systems
Exponential Runge-Kutta methods for parabolic problems.
Embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators
On the stability of exponential integrators for non-diffusive equations
A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
Explicit pseudo two-step exponential Runge-Kutta methods for the numerical integration of first-order differential equations
Exponential collocation methods for conservative or dissipative systems
Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems
Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
Structure-Preserving Algorithms for Oscillatory Differential Equations II
Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems
Exponential integrators
Second Derivative Extended Backward Differentiation Formulas for the Numerical Integration of Stiff Systems
On Krylov Subspace Approximations to the Matrix Exponential Operator
Exponential Integrators for Large Systems of Differential Equations
Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
Exponential Fourier Collocation Methods for Solving First-Order Differential Equations
Structure-Preserving Algorithms for Oscillatory Differential Equations
Geometric Integrators for Differential Equations with Highly Oscillatory Solutions
Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems
Geometric Numerical Integration
B-series and Order Conditions for Exponential Integrators
Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
Multistep Methods with Variable Matrix Coefficients
Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
Trapezoidal Methods of Approximating Solutions of Differential Equations
Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
Two new classes of exponential Runge–Kutta integrators for efficiently solving stiff systems or highly oscillatory problems

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