Convergence analysis of two conservative finite difference fourier pseudo-spectral schemes for klein-Gordon-Dirac system

Wang, Xianfen; Li, Jiyong

doi:10.1016/j.amc.2022.127634

Cited by 2 publications

(1 citation statement)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In practical application, efficient numerical methods are very necessary. Existing numerical methods include finite difference (FD) and compact FD (CFD) methods [8,12,31,41,44], exponential wave integrator (EWI) methods [27,44], time-splitting (TS) methods [42,45]. Generally speaking, compared with the FD and CFD methods, these EWI methods and TS methods perform better in numerical accuracy and regularity requirement.…”

Section: Introductionmentioning

confidence: 99%

Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant

2023

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

We provide improved uniform error estimates for the time‐splitting Fourier pseudo‐spectral (TSFP) methods applied to the Klein–Gordon–Dirac system (KGDS) with the small parameter . We first reformulate the KGDS into a coupled Schrödinger–Dirac system (CSDS) and then apply the second‐order Strang splitting method to CSDS with the spatial discretization provided by Fourier pseudo‐spectral method. Based on rigorous analysis, we establish improved uniform error bounds for the second‐order Strang splitting method at up to the long time at . In addition to the conventional analysis methods, we mainly apply the regularity compensation oscillation technique for the analysis of long time dynamic simulation. The numerical results show that our method and conclusion are not only suitable for one‐dimensional problem, but also can be directly extended to higher dimensional problem and highly oscillatory problem. As far as we know there has not been any relevant long time analysis and any improved uniform error bounds for the TSFP method solving the KGDS. Our methods are novel and provides a reference for analyzing the improved error bounds of other coupled systems similar to the KGDS.

show abstract

Section: Introductionmentioning

confidence: 99%

Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant

2023

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

show abstract

Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation

2023

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

Convergence analysis of two conservative finite difference fourier pseudo-spectral schemes for klein-Gordon-Dirac system

Cited by 2 publications

References 30 publications

Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant

Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant

Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation

Contact Info

Product

Resources

About