Abstract
We present finite difference schemes for the one-dimensional Chern-Simons gauged Schrödinger and Dirac equations. We provide two numerical schemes for the Chern-Simons-Schrödinger equations, each of them has its own advantage in total charge preservation and the second-order accuracy. On the other hand, we offer the second-order, total charge-preserving numerical scheme for the Chern-Simons-Dirac equations. We numerically test each method and validate the total charge preserving properties. We also compare the solutions to the Chern-Simons gauged equations with the equations without the gauge effect, illustrating the effect of gauge fields on the dynamics of the matter field.
| Original language | English |
|---|---|
| Pages (from-to) | 6417-6439 |
| Number of pages | 23 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 27 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - Nov 2022 |
Bibliographical note
Publisher Copyright:© 2022 American Institute of Mathematical Sciences. All rights reserved.
Keywords
- Chern-Simons-Dirac equations
- Chern-Simons-Schrödinger equations
- finite difference method
- total charge preservation
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