Parallel solution in time of ODEs: Some achievements and perspectives

DOI10.1016/j.apnum.2008.03.024zbMath1166.65349OpenAlexW2171063948MaRDI QIDQ1007365

Luigi Brugnano, Pierluigi Amodio

Publication date: 20 March 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.03.024

zbMATH Keywords

ordinary differential equationsinitial value problemsparallel computingstiff problems``Parareal algorithmblock one step methodsboundary value methods (BVMs)parallel factorizationsparallel methods ``in time for ODEs

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (10)

Interweaving PFASST and Parallel Multigrid ⋮ Time-parallel solutions to differential equations via functional optimization ⋮ A parareal waveform relaxation algorithm for semi-linear parabolic partial differential equations ⋮ Convergence of block boundary value methods for solving delay differential algebraic equations with index-1 and index-2 ⋮ An enhanced parareal algorithm based on the deferred correction methods for a stiff system ⋮ Parallel exponential Rosenbrock methods ⋮ A parallel spectral deferred correction method for first-order evolution problems ⋮ Wave propagation characteristics of Parareal ⋮ 50 Years of Time Parallel Time Integration ⋮ Parareal for Diffusion Problems with Space- and Time-Dependent Coefficients

Uses Software

• ParalleloGAM
• BABDCR

Cites Work

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• The parallel QR factorization algorithm for tridiagonal linear systems
• Parallel implementation of block boundary value methods for ODEs
• A parareal in time procedure for the control of partial differential equations
• Parallel factorizations and parallel solvers for tridiagonal linear systems
• ParalleloGAM: A parallel code for ODEs
• Parallel ODE solvers based on block BVMs
• On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs)
• RD-rational approximations of the matrix exponential
• Résolution d'EDP par un schéma en temps «pararéel »
• Computational chemistry from the perspective of numerical analysis
• Nonlinear Convergence Analysis for the Parareal Algorithm
• Algorithm 859
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Parallel Factorizations for Tridiagonal Matrices
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• Parallel methods for ODEs

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