Jahnke T. Splitting methods for evolution equations 2025

Textbook in PDF format

Motivation
Splitting methods for discretized Schrödinger equations
Splitting methods for Hamiltonian systems
Advantages of splitting methods and topics of this lecture
Splitting methods for ordinary differential equations
Preliminaries
Symmetric methods
Order of splitting and composition methods
Splitting methods for linear Schrödinger equations
The linear Schrödinger equation
Splitting methods
Error analysis for the space discretization
Semigroup theory, part
Abstract error analysis
Application to the linear Schrödinger equation
Splitting methods for nonlinear Schrödinger equations
Problem setting and main results
Stability: Proof of Proposition
Local error in H1 (T): Proof of Proposition
Local error in L2 (T): Sketch of the proof of Proposition
Global error: Proof of Theorem
Dimension splitting methods for parabolic problems
Dimension splitting methods
Semigroup theory, part
Analytic setting
Error analysis
Gronwall’s lemma
Sobolev spaces