Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Parallel factorizations for tridiagonal matrices
SIAM Journal on Numerical Analysis
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
The parallel QR factorization algorithm for tridiagonal linear systems
Parallel Computing
Parallel implementation of block boundary value methods for ODEs
Journal of Computational and Applied Mathematics
On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs)
Applied Numerical Mathematics - Special issue on time integration
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
ParalleloGAM: a parallel code for ODEs
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Algorithm 859: BABDCR—a Fortran 90 package for the solution of bordered ABD linear systems
ACM Transactions on Mathematical Software (TOMS)
Analysis of the Parareal Time-Parallel Time-Integration Method
SIAM Journal on Scientific Computing
A parareal waveform relaxation algorithm for semi-linear parabolic partial differential equations
Journal of Computational and Applied Mathematics
An enhanced parareal algorithm based on the deferred correction methods for a stiff system
Journal of Computational and Applied Mathematics
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The parallel solution of initial value problems for ordinary differential equations (ODE-IVPs) has received much interest from many researchers in the past years. In general, the possibility of using parallel computing in this setting concerns different aspects of the numerical solution of ODEs, depending on the parallel platform to be used and/or the complexity of the problem to be solved. In particular, in this paper we examine possible extensions of a parallel method previously proposed in the mid-nineties [P. Amodio, L. Brugnano, Parallel implementation of block boundary value methods for ODEs, J. Comput. Appl. Math. 78 (1997) 197-211; P. Amodio, L. Brugnano, Parallel ODE solvers based on block BVMs, Adv. Comput. Math. 7 (1997) 5-26], and analyze its connections with subsequent approaches to the parallel solution of ODE-IVPs, in particular the ''Parareal'' algorithm proposed in [J.L. Lions, Y. Maday, G. Turinici, Resolution d'EDP par un schema en temps ''parareel'', C. R. Acad. Sci. Paris, Ser. I 332 (2001) 661-668; Y. Maday, G. Turinici, A parareal in time procedure for the control of partial differential equations, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 387-392].