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

Symmetric and arbitrarily high-order Birkhoff–Hermite time integrators and their long-time behaviour for solving nonlinear Klein–Gordon equations

(2018) Changying Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Trigonometric integrators for quasilinear wave equations

(2018) Ludwig Gauckler et al.   MATHEMATICS OF COMPUTATION

Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations

(2017) Bin Wang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

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

(2017) Changying Liu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type

(2017) Balázs Kovács et al.   NUMERISCHE MATHEMATIK

Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations

(2016) Bin Wang et al.   CALCOLO

Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations

(2016) Marlis Hochbruck et al.   NUMERISCHE MATHEMATIK

Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems

(2016) Yu-Wen Li et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Arbitrary-Order Trigonometric Fourier Collocation Methods for Multi-Frequency Oscillatory Systems

(2015) Bin Wang et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Error Analysis of Trigonometric Integrators for Semilinear Wave Equations

(2015) Ludwig Gauckler   SIAM JOURNAL ON NUMERICAL ANALYSIS

Conservation of invariants by symmetric multistep cosine methods for second-order partial differential equations

(2012) B. Cano   BIT NUMERICAL MATHEMATICS

Operator splitting for partial differential equations with Burgers nonlinearity

(2012) Helge Holden et al.   MATHEMATICS OF COMPUTATION

Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations

(2012) Mechthild Thalhammer   SIAM JOURNAL ON NUMERICAL ANALYSIS

Analysis and comparison of numerical methods for the Klein–Gordon equation in the nonrelativistic limit regime

(2011) Weizhu Bao et al.   NUMERISCHE MATHEMATIK

ERKN integrators for systems of oscillatory second-order differential equations

(2010) Xinyuan Wu et al.   COMPUTER PHYSICS COMMUNICATIONS

Convergence of a split-step Hermite method for the Gross-Pitaevskii equation

(2010) L. Gauckler   IMA JOURNAL OF NUMERICAL ANALYSIS

Variational-splitting time integration of the multi-configuration time-dependent Hartree-Fock equations in electron dynamics

(2010) O. Koch et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Exponential integrators

(2010) Marlis Hochbruck et al.   ACTA NUMERICA

Exponential Rosenbrock-Type Methods

(2009) Marlis Hochbruck et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Multistep cosine methods for second-order partial differential systems

(2008) B. Cano et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations

(2008) Christian Lubich   MATHEMATICS OF COMPUTATION

Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations

(2008) David Cohen et al.   NUMERISCHE MATHEMATIK