Relaxation Exponential Rosenbrock-Type Methods for Oscillatory Hamiltonian Systems

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for stiff equations (65L04)

Cites Work

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An adaptive meshless local Petrov-Galerkin method based on a posteriori error estimation for the boundary layer problems
Fourth-order two-stage explicit exponential integrators for time-dependent PDEs
A simple framework for the derivation and analysis of effective one-step methods for ODEs
Generalized integrating factor methods for stiff PDEs
Highly stable implicit-explicit Runge-Kutta methods
Relaxation Runge-Kutta methods for Hamiltonian problems
Implementation of exponential Rosenbrock-type integrators
Higher-order additive Runge-Kutta schemes for ordinary differential equations
Parallel exponential Rosenbrock methods
Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions
Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
Linearly implicit and high-order energy-conserving schemes for nonlinear wave equations
General relaxation methods for initial-value problems with application to multistep schemes
Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field
Exponential Rosenbrock methods of order five -- construction, analysis and numerical comparisons
Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems
IMEX Runge-Kutta schemes for reaction-diffusion equations
High-order multi-symplectic schemes for the nonlinear Klein-Gordon equation
Time integration and discrete Hamiltonian systems
Efficient exponential time integration for simulating nonlinear coupled oscillators
Linearly implicit and high-order energy-preserving relaxation schemes for highly oscillatory Hamiltonian systems
Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems
Exponential integrators
Line Integral Methods for Conservative Problems
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
Stability of Runge-Kutta Methods for Trajectory Problems
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
Geometric integration using discrete gradients
Exponential Integrators for Large Systems of Differential Equations
Maximum norm analysis of implicit–explicit backward difference formulae for nonlinear parabolic equations
Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
Implicit–explicit multistep methods for nonlinear parabolic equations
Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle
Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs
Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems
Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms
Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
Exponential Rosenbrock-Type Methods
A new class of energy-preserving numerical integration methods
Geometric Numerical Integration
Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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