arXiv subjects

Zhirui Shen

Publications and source records attributed to Zhirui Shen.

3 recordsLinked to original sources

arXiv2026

A Curve-Reference Exponential Integrator for Three-Dimensional Charged-Particle Dynamics under a Strong Nonconstant Magnetic Field

We study a three-dimensional charged-particle dynamics model in the nonrelativistic momentum formulation and construct a curve-reference exponential integrator (CREI) for this system. Since the zero eigenvalue of linear section is not semisimple, the system after usual change of variables does not meet the spectral condition used in the classical locally linearized extended exponential integrator (LLEEI). A kernel-range decomposition of the dominant magnetic matrix and a further linear transformation reduce the equation to a system with a semisimple zero block and one constant skew-symmetric oscillatory block. The CREI expands the nonlinear term along the exact oscillatory curve rather than at a fixed point. Retaining monomials through degree k defines CREI(k + 1). We prove uniform local and global error bounds and present reproducible numerical experiments for convergence in h and uniformity in ε.

math.NA↗

arXiv2026

An Explicit Symmetric Exponential Integrator and Its Error Estimate for the Relativistic Charged-Particle Dynamics

This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an explicit symmetric exponential integrator based on Lie splitting. Rigorous analysis establishes its unconditional stability and second-order convergence. Numerical experiments confirm its superior performance, including accuracy, effciency and long-time Hamiltonian conservation.

math.NA↗

arXiv2026

Explicit symmetric low-regularity integrators for the semilinear Klein-Gordon equation

This paper is concerned with the design and analysis of symmetric low-regularity integrators for the semilinear Klein-Gordon equation. We first propose a general symmetrization procedure that allows for the systematic construction of symmetric schemes from existing explicit (non-symmetric) integrators. Applying this procedure, we derive two novel schemes. Error analyses show that both integrators achieve their optimal convergence orders in the energy space under significantly relaxed regularity assumptions. Furthermore, the symmetry property ensures that the convergence order of a first-order symmetric scheme improves as the regularity of the exact solution increases. A numerical experiment demonstrates that the proposed second-order symmetric scheme nearly preserves the system energy over extended periods.

math.NA↗