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Chapter 5 : Direct Space Time Parallel Solvers

Section 5.1 : Parallel Predictor Corrector Methods

📜 Description	🧮 Matlab	🐍 Python
Predictor-Corrector scheme from Mikanker and Liniger, sequential	MirakerLinigerS.m	MirakerLinigerS.py
Predictor-Corrector scheme from Mikanker and Liniger, parallel	MirakerLinigerP.m	MirakerLinigerP.py
Example of use on the Lorenz system	exampleMirankerLiniger.m	exampleMirankerLiniger.py

Section 5.3 : Time Parallel Cyclic Reduction

📜 Description	🧮 Matlab	🐍 Python
Cyclic Reduction for a bidiagonal system	CyclicReduction.m	CyclicReduction.py
Cyclic Reduction for a bidiagonal system	CyclicBackSubstitution.m	CyclicBackSubstitution.py
example of use on Dahlquist equation	exampleCyclicReductionDahlquist.m	exampleCyclicReductionDahlquist.m

🔔 The code for CyclicReduction given in the book is incomplete, the version above is the correct one.

Section 5.4 : Time Parallel Methods Based on Laplace Transform

📜 Description	🧮 Matlab	🐍 Python
Time-Parallel Laplace Transform on the Heat equation	exampleLaplaceTransform.m	exampleLaplaceTransform.py

Section 5.5 : Time Parallelization Based on Diagonalization

📜 Description	🧮 Matlab	🐍 Python
Paradiag-I with Backward Euler to solve the ODE $y'+ay(t)=f(t)$	ODEBEP.m	ODEBEP.py
Paradiag-II applied on the Dahlquist problem	exampleDirectDahlquist.m	exampleDirectDahlquist.py

Section 5.6 : Time Parallelization Based on Integral Deferred Corrections

📜 Description	🧮 Matlab	🐍 Python
Lagrange Weights in IDC for $M \in {2, 3, 4, 5, 6}$	LagrangeWeights.m	LagrangeWeights.py
Integral Deferred Corrections	IDC.m	IDC.py
example of IDC on the Dahlquist problem	exampleIDCDahlquist.m	exampleIDCDahlquist.py
Parallel Integral Deferred Corrections	PIDC.m	PIDC.py
Revisionist Integral Deferred Corrections	RIDC.m	RIDC.py
Revisionist Integral Deferred Corrections with Restarts	RIDCRestarts.m	RIDCRestarts.py

Section 5.7 : ParaExp

📜 Description	🧮 Matlab	🐍 Python
ParaExp used to solve the Heat equation in Matlab	exampleParaExp.m	exampleParaExp.py

📖 Table of Content