Splitting Methods for Differential Equations

Sergio Blanes, Fernando Casas, Ander Murua, Acta Numerica 2024

Supplementary Material

Contents 1 Introduction 2 High order splitting and composition methods 3 Splitting methods for special problems 4 Qualitative properties of splitting methods 5 Highly oscillatory problems 6 Splitting methods for PDEs 7 Splitting methods with complex coefficients 8 A collection of splitting methods 9 Splitting everywhere: some relevant applications References A Testing splitting methods on matrices

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Page Last Updated: 14 December, 2023

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1- MATLAB files containing most of the splitting and composition methods gathered in Section 8

• (a) Methods of Table 8.1: Symmetric compositions of second-order symmetric schemes of order r = 4, 6, 8, 10

• Non-processed schemes:
coefsSS.m
• Processed schemes:
coefsSSproc.m

• (b) Methods of Table 8.2: Splitting methods of order r = 2, 3, 4, 6

• Non-processed schemes:
coefsS.m
• Processed schemes:
coefsSproc.m

• (c) Methods of Table 8.3: RKN splitting methods of order r = 4, 5, 6, 8

• Non-processed schemes:
coefsRKN.m
• Processed schemes:
coefsRKNproc.m

• (d) Methods of Table 8.4: RKN splitting methods of order r = 4, 6, 8 with modified potentials / double commutators

• Non-processed schemes:
coefsRKNmod.m
• Processed schemes:
coefsRKNmod_proc.m

• (e) Methods of Table 8.5: Splitting methods for near-integrable systems

• Non-processed schemes:
coefsNI.m
• Processed schemes:
coefsNIproc.m