ParalleloGAM: A parallel code for ODEs. The method uses the “parallelism across the steps”. It extends a previous paper of the authors [J. Comput. Appl. Math. 78, No. 2, 197-211 (1997; Zbl 0868.65039)] to nonlinear problems and is closely related to a companion paper of L. Brugnano and D. Trigiante [Appl. Numer. Math. 28, No. 1-4, 127-141 (1998; reviewed below)] for the theory. In a first coarse step the grid is determined (only 3 processors active). Then the linear system resulting from the Newton iteration is factored (block diagonal) and solved on p processors. Analysis of operations and numerical tests compared to a sequential Radau code. The parallel version wins only for higher accuracy (many steps).
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References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
- Kumar, Surendra; Sharma, Abhishek; Pal Singh, Harendra: Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay (2021)
- Amodio, Pierluigi; Brugnano, Luigi: Parallel solution in time of ODEs: Some achievements and perspectives (2009)
- Brugnano, Luigi: Blended block BVMs (B(_3)VMs): A family of economical implicit methods for ODEs (2000)
- Iavernaro, F.; Mazzia, F.: Block-boundary value methods for the solution of ordinary differential equations (1999)
- Amodio, Pierluigi; Brugnano, Luigi: ParalleloGAM: A parallel code for ODEs (1998)
- Brugnano, Luigi; Trigiante, Donato: Parallel implementation of block boundary value methods on nonlinear problems: Theoretical results (1998)
- Amodio, Pierluigi; Brugnano, Luigi: Parallel implementation of block boundary value methods for ODEs (1997)
- Amodio, Pierluigi; Mazzia, Francesca: Numerical solution of differential algebraic equations and computation of consistent initial/boundary conditions (1997)
- Brugnano, Luigi; Trigiante, Donata: On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs) (1997)