Iterative operator-splitting methods for unbounded operators: Error analysis and examples

TL;DR

This paper introduces an iterative operator-splitting method for unbounded operators, providing error bounds and demonstrating its application to differential and Schrödinger equations.

Contribution

It develops error analysis for iterative splitting methods involving unbounded operators and demonstrates their effectiveness through practical examples.

Findings

Error bounds for iterative splitting with unbounded operators derived

Method applicable to hyperbolic and parabolic equations

Successful application to differential and Schrödinger equations

Abstract

In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of hyperbolic and parabolic type are allowed and discussed in the applications. Mixed experiments are applied to ordinary differential equations and evolutionary Schr\"odinger equations.