An Explicit Hermite-Taylor Method for the Schrödinger Equation (Communications in Computational Physics, 2018)
An explicit spectrally accurate order-adaptive Hermite-Taylor method forthe Schrödinger equation is developed. Numerical experiments illustrating the propertiesof the method are presented. The method, which is able to use very coarse gridswhile still retaining high accuracy, compares favorably to an existing exponential integrator– high order summation-by-parts finite difference method.