Exact splitting methods for kinetic and Schr{\"o}dinger equations

TL;DR

This paper combines exact splitting methods with pseudo-spectral spatial discretization to solve kinetic and Schrödinger equations, demonstrating high accuracy and efficiency.

Contribution

It introduces a novel combination of exact splitting techniques with pseudo-spectral methods for improved numerical solutions of kinetic and Schrödinger equations.

Findings

High accuracy achieved with combined methods

Efficient computation demonstrated

Applicable to inhomogeneous quadratic differential equations

Abstract

In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact splittings are combined with pseudo-spectral methods in space to illustrate their high accuracy and efficiency.