Embedded exponential Runge-Kutta-Nyström methods for highly oscillatory Hamiltonian systems (Q6589887)

scientific article; zbMATH DE number 7898992

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English	Embedded exponential Runge-Kutta-Nyström methods for highly oscillatory Hamiltonian systems	scientific article; zbMATH DE number 7898992

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instance of

scholarly article

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title

Embedded exponential Runge-Kutta-Nyström methods for highly oscillatory Hamiltonian systems (English)

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Journal of Computational Physics

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publication date

20 August 2024

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zbMATH Keywords

exponential RKN method

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embedded methods

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highly oscillatory Hamiltonian systems

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variable stepsize

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MaRDI profile type

Publication

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cites work

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Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations

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A Gautschi-type method for oscillatory second-order differential equations

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Exponentially fitted explicit Runge-Kutta-Nyström methods

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Exponentially fitted Runge-Kutta methods

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Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators

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New methods for oscillatory systems based on ARKN methods

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ERKN integrators for systems of oscillatory second-order differential equations

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Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods

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Extended RKN-type methods for numerical integration of perturbed oscillators

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Explicit symplectic RKN methods for perturbed non-autonomous oscillators: splitting, extended and exponentially fitting methods

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An Essential Extension of the Finite-Energy Condition for Extended Runge-Kutta-Nyström Integrators when Applied to Nonlinear Wave Equations

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The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications

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Efficient energy-preserving integrators for oscillatory Hamiltonian systems

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An extended discrete gradient formula for oscillatory Hamiltonian systems

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Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems

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Continuous trigonometric collocation polynomial approximations with geometric and superconvergence analysis for efficiently solving semi-linear highly oscillatory hyperbolic systems

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Global error bounds of one-stage extended RKN integrators for semilinear wave equations

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Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations

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Extended RKN methods with FSAL property for oscillatory systems

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Embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators

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Optimized pairs of multidimensional ERKN methods with FSAL property for multi-frequency oscillatory systems

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KIOPS: a fast adaptive Krylov subspace solver for exponential integrators

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Exponential Rosenbrock-Type Methods

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New Adaptive Exponential Propagation Iterative Methods of Runge--Kutta Type

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Embedded paired explicit Runge-Kutta schemes

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Adaptive IMEX schemes for high-order unstructured methods

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Exponential time-differencing with embedded Runge-Kutta adaptive step control

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Semi-analytical exponential RKN integrators for efficiently solving high-dimensional nonlinear wave equations based on FFT techniques

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New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form \(y''=f(x,y)\)

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High-Order Embedded Runge-Kutta-Nystrom Formulae

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High Phase-Lag-Order Runge--Kutta and Nyström Pairs

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A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators.

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A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems

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Solving Ordinary Differential Equations I

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Efficient implementation of the ARKN and ERKN integrators for multi-frequency oscillatory systems with multiple time scales

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Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions

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Spectral Methods

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Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme

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The solution of the two-dimensional sine-Gordon equation using the method of lines

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Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2024.113221

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Sitelinks

Mathematics(1 entry)

mardi Publication:6589887