107 citations · 334 across the 17 of their papers we have counts for
17 papers
Two new classes of exponential Runge-Kutta integrators for efficiently solving stiff systems or highly oscillatory problems
Bin Wang, Xianfa Hu, Xinyuan Wu
We note a fact that stiff systems or differential equations that have highly oscillatory solutions cannot be solved efficiently using conventional methods. In this paper, we study…
General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
Yuwen Li, Xinyuan Wu
In this paper we propose and investigate a general approach to constructing local energy-preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonia…
Functionally-fitted energy-preserving methods for solving oscillatory nonlinear Hamiltonian systems
Yu-Wen Li, Xinyuan Wu
In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and many researchers have been concerned with the design and analysi…
Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems
Yu-Wen Li, Xinyuan Wu
In this paper, combining the ideas of exponential integrators and discrete gradients, we propose and analyze a new structure-preserving exponential scheme for the conservative or d…
A two-step symmetric method for charged-particle dynamics in a normal or strong magnetic feld
Bin Wang, Xinyuan Wu, Yonglei Fang
The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze…
Long-time momentum and actions behaviour of energy-preserving methods for semilinear wave equations via spatial spectral semi-discretizations
Bin Wang, Xinyuan Wu
As is known that wave equations have physically very important properties which should be respected by numerical schemes in order to predict correctly the solution over a long time…
Long-time oscillatory energy conservation of total energy-preserving methods for highly oscillatory Hamiltonian systems
Bin Wang, Xinyuan Wu
For an integrator when applied to a highly oscillatory system, the near conservation of the oscillatory energy over long times is an important aspect. In this paper, we study the l…
Volume-preserving exponential integrators
Bin Wang, Xinyuan Wu
As is known that various dynamical systems including all Hamiltonian systems preserve volume in phase space. This qualitative geometrical property of the analytical solution should…
Long-term analysis of symplectic or symmetric extended RKN methods for nonlinear wave equations
Bin Wang, Xinyuan Wu
This paper analyses the long-time behaviour of one-stage symplectic or symmetric extended Runge--Kutta--Nyström (ERKN) methods when applied to nonlinear wave equations. It is shown…
Long-time analysis of extended RKN integrators for Hamiltonian systems with a solution-dependent high frequency
Bin Wang, Xinyuan Wu
In this paper, we analyse the long-time behaviour of the extended RKN (ERKN) integrators for solving highly oscillatory Hamiltonian systems with a slowly varying, solution-dependen…
Exponential collocation methods for the cubic Schrödinger equation
Bin Wang, Xinyuan Wu
In this paper we derive and analyse new exponential collocation methods to efficiently solve the cubic Schrödinger Cauchy problem on a -dimensional torus. Energy preservation is…
Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations
Bin Wang, Xinyuan Wu
In this paper, we present an error analysis of one-stage explicit extended Runge--Kutta--Nyström integrators for semilinear wave equations. These equations are analysed by using sp…
Functionally-fitted energy-preserving integrators for Poisson systems
Bin Wang, Xinyuan Wu
In this paper, a new class of energy-preserving integrators is proposed and analysed for Poisson systems by using functionally-fitted technology. The integrators exactly preserve e…
Exponential collocation methods for conservative or dissipative systems
Bin Wang, Xinyuan Wu
In this paper, we propose and analyse a novel class of exponential collocation methods for solving conservative or dissipative systems based on exponential integrators and collocat…
A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems
Bin Wang, Xinyuan Wu
The primary objective of this paper is to present a long-term numerical energy-preserving analysis of one-stage explicit symmetric and/or symplectic extended Runge--Kutta--Nyström…
Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
Bin Wang, Xinyuan Wu, Fanwei Meng
In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order d…
Exponential Fourier collocation methods for solving first-order differential equations
Bin Wang, Xinyuan Wu, Fanwei Meng +1
In this paper, a novel class of exponential Fourier collocation methods (EFCMs) is presented for solving systems of first-order ordinary differential equations. These so-called exp…