光学Bloch方程的数值解法

用常微分方程的经典数值解法Euler法、Heun法、标准四阶Runge-Kutta法和修正四阶预报-校正法求解光学Bloch方程,并与一定条件下的解析解进行了比较,分析了四种算法,尤其是修正四阶预报-校正算法的误差与可靠性.计算的结果表明,四种数值算法在合适步长下,对光学Bloch方程的求解都可以收敛,并能保持算法所具有的相应误差阶数.验证了四阶预报-校正算法的可靠性以及在光学Bloch方程分析光学瞬态相干过程中的应用.该方法对求解光学Bloch方程具有普适意义.

Numerical Methods for Optical Bloch Equations

The classical numerical treatments of ordinary differential equations, including Eider, Heun, fourth-order Runge-Kutta and a new fourth-order predictor-corrector methods, are used to solve the optical Bloch equations. By comparing the numerical results and with analytical results, the four numerical methods, especially for the new method's errors and reliability are analyzed. The numerical results prove that, if the steps are suitable, the four numerical methods for the Bloch equations are possible convengence and can keep the numerical method's corresponding errors. The new method is reliable, can be used to optical transient coherent process, and is significant for solving the optical Bloch equations.