On nested Picard iterative integrators for highly oscillatory second-order differential equations
type: Item
instance of: scholarly article
title: On nested Picard iterative integrators for highly oscillatory second-order differential equations
zbMATH Open document ID: 1504.65159
author: Yan Wang
published in: Numerical Algorithms
publication date: 2022-11-22T00:00:00Z
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 7621827
zbMATH Keywords: highly oscillatory differential equations
zbMATH Keywords: uniformly accurate
zbMATH Keywords: error bound
zbMATH Keywords: nested Picard iteration
zbMATH Keywords: super convergence
zbMATH Keywords: Klein-Gordon equation
MaRDI profile type: Publication
full work available at URL: s11075-022-01317-8
OpenAlex ID: W4229041077
Wikidata QID: Q115381560
cites work: A multiscale method for highly oscillatory ordinary differential equations with resonance
cites work: Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime
cites work: Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
cites work: A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime
cites work: Uniformly Accurate Multiscale Time Integrators for Highly Oscillatory Second Order Differential Equations
cites work: Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting
cites work: Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime
cites work: Stroboscopic averaging for the nonlinear Schrödinger equation
cites work: Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
cites work: Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems
cites work: Modulated Fourier expansions of highly oscillatory differential equations
cites work: Numerical energy conservation for multi-frequency oscillatory differential equations
cites work: Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations
cites work: On highly oscillatory problems arising in electronic engineering
cites work: On second-order differential equations with highly oscillatory forcing terms
cites work: Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation
cites work: Heterogeneous multiscale methods for stiff ordinary differential equations
cites work: Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
cites work: Long-Time-Step Methods for Oscillatory Differential Equations
cites work: Error Analysis of Trigonometric Integrators for Semilinear Wave Equations
cites work: Numerical integration of ordinary differential equations based on trigonometric polynomials
cites work: Error analysis of exponential integrators for oscillatory second-order differential equations
cites work: Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
cites work: Geometric Numerical Integration
cites work: A Gautschi-type method for oscillatory second-order differential equations
cites work: Exponential integrators
cites work: On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
cites work: Adiabatic integrators for highly oscillatory second-order linear differential equations with time-varying eigendecomposition
cites work: Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations
cites work: From nonlinear Klein-Gordon equation to a system of coupled nonlinear Schrödinger equations
cites work: The nonrelativistic limit of the nonlinear Klein-Gordon equation
cites work: Low regularity exponential-type integrators for semilinear Schrödinger equations
cites work: Mollified Impulse Methods for Highly Oscillatory Differential Equations
cites work: Modulated Fourier expansions and heterogeneous multiscale methods
cites work: Low-regularity integrators for nonlinear Dirac equations
cites work: Numerical solution of a nonlinear Klein-Gordon equation
cites work: Q5475508
cites work: Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions
cites work: Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems
cites work: Analysis of the heterogeneous multiscale method for ordinary differential equations
cites work: Q3538693
cites work: Uniformly accurate multiscale time integrators for second order oscillatory differential equations with large initial data
DOI: 10.1007/S11075-022-01317-8
Recommended article: Uniformly accurate nested Picard integrators for a system of oscillatory ordinary differential equations
Recommended article: A new numerical method for the integration of highly oscillatory second-order ordinary differential equations
Recommended article: Asymptotic-numerical solvers for highly oscillatory second-order differential equations
Recommended article: Some numerical algorithms for solving the highly oscillatory second-order initial value problems
Recommended article: Q5352139
Recommended article: Q4263447
Recommended article: Uniformly accurate nested Picard iterative schemes for nonlinear Schrödinger equation with highly oscillatory potential
Recommended article: Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs
Recommended article: An explicit Numerov-type method for second-order differential equations with oscillating solutions
Recommended article: New explicit adapted Numerov methods for second-order oscillatory differential equations
description: scientific article; zbMATH DE number 7621827