In (Bernier in Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators. arXiv:1912.13219, (2019)), some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, Fokker–Planck equations, and Schrödinger type equations with an angular momentum rotation term. In this work, these exact splittings are used combined with pseudo-spectral methods in space. High accuracy and efficiency of exact splitting methods are illustrated and comparison are performed with the numerical methods in literature. We show that our methods can be used to improve significantly some classical splitting methods for some nonlinear or non-quadratic equations.

在（对于不均匀二次微分算子生成的半群的精确分裂方法Bernier.arXiv：1912.13219，（2019））中，提出了一些非均匀二次微分方程的精确分离方法，例如输运方程，Fokker-Planck方程和Schrödinger角动量旋转项的类型方程。在这项工作中，这些精确的分裂与空间中的伪光谱方法结合使用。说明了精确分割方法的高精度和高效率，并与文献中的数值方法进行了比较。我们表明，我们的方法可用于显着改进一些非线性或非二次方程的经典分裂方法。