We propose a Lawson-time-splitting extended Fourier pseudospectral (LTSeFP) method for the numerical integration of the Gross-Pitaevskii equation with time-dependent potential that is of low regularity in space. For the spatial discretization of low regularity potential, we use an extended Fourier pseudospectral (eFP) method, i.e., we compute the discrete Fourier transform of the low regularity potential in an extended window. For the temporal discretization, to efficiently implement the eFP method for time-dependent low regularity potential, we combine the standard time-splitting method with a Lawson-type exponential integrator to integrate potential and nonlinearity differently. The LTSeFP method is both accurate and efficient: it achieves first-order convergence in time and optimal-order convergence in space in $L^2$-norm under low regularity potential, while the computational cost is comparable to the standard time-splitting Fourier pseudospectral method. Theoretically, we also prove such convergence orders for a large class of spatially low regularity time-dependent potential. Extensive numerical results are reported to confirm the error estimates and to demonstrate the superiority of our method.

翻译：我们提出了一种Lawson时间分裂扩展傅里叶伪谱（LTSeFP）方法，用于数值求解具有空间低正则性时间依赖势的Gross-Pitaevskii方程。针对低正则势的空间离散，我们采用扩展傅里叶伪谱（eFP）方法，即在扩展窗口内计算低正则势的离散傅里叶变换。在时间离散方面，为高效实现含时间依赖低正则势的eFP方法，我们将标准时间分裂法与Lawson型指数积分器相结合，以不同方式处理势函数和非线性项。LTSeFP方法兼具精确性与高效性：在低正则势条件下，该方法在$L^2$范数下达到时间一阶收敛和空间最优阶收敛，而计算成本与标准时间分裂傅里叶伪谱方法相当。理论上，我们针对一大类空间低正则时间依赖势证明了上述收敛阶。大量数值实验结果验证了误差估计，并展示了本方法的优越性。