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Abstract: We describe a MIMD parallel code to solve a general class of ordinary differential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of parabolic partial differential equations. The main goals of this work are sharp bounds on the accuracy of the computed solution and flexibility of the software. We discuss the sources of error in solving differential equations, and the resulting constraints on time steps. We also discuss the theory of... (Update)
Context of citations to this paper: More
.... of slow motion is actually possible, compare for example Estep [18] Estep, Verduyn Lunel, and Williams [19] Estep and Williams [20], as well as Reyna and Ward [39] As the number of references attests, much analysis has been devoted to the study of slow motion of...
.... of slow motion is actually possible, compare for example Estep [23] Estep, Verduyn Lunel, and Williams [24] Estep and Williams [25], as well as Reyna and Ward [49] As the number of references attests, much analysis has been devoted to the study of slow motion of...
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0.3: An S-I-R Model for Epidemics with Diffusion to Avoid Infection .. - Meade, Milner (Correct)
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BibTeX entry: (Update)
D. J. Estep and R. D. Williams. Accurate parallel integration of large sparse systems of differential equations. Mathematical Models & Methods in Applied Sciences, 6:535--568, 1996. http://citeseer.ist.psu.edu/estep96accurate.html More
@misc{ estep96accurate,
author = "D. Estep and R. Williams",
title = "Accurate parallel integration of large sparse systems of differential equations",
text = "D. J. Estep and R. D. Williams. Accurate parallel integration of large
sparse systems of differential equations. Mathematical Models & Methods
in Applied Sciences, 6:535--568, 1996.",
year = "1996",
url = "citeseer.ist.psu.edu/estep96accurate.html" }
Citations (may not include all citations):715 GMRES: A generalized minimal residual algorithm for solving .. (context) - Saad, Schultz - 1986
257 QMR: A quasi-minimal residual method for nonHermitian linear.. - Freund, Nachtigal - 1991
144 Performance of Dynamic load balancing algorithms for unstruc.. - Williams - 1991
96 Parallel Computing Works (context) - Fox, Williams et al. - 1994
83 Adaptive finite element methods for parabolic problems IV: n.. - Eriksson, Johnson - 1992
83 Adaptive finite-element methods for parabolic problems - Eriksson, Johnson - 1991
38 Iterative solution of linear equations in ODE codes (context) - Gear, Saad - 1983
29 Complex patterns in a simple system (context) - Pearson - 1993
21 A globally convergent matrix-free algorithm for implicit tim.. (context) - Johan, Hughes et al. - 1991
19 DIME: Distributed Irregular Mesh Environment - Williams
18 Motion by mean-curvature as the singular limit of Ginzburg-L.. (context) - Bronsard, Kohn - 1991
17 Matrix-free methods for stiff systems of ODE's (context) - Brown, Hindmarsh - 1986
16 An analysis of the composite step bi-conjugate gradient meth.. - Bank, Chan - 1993
12 Computation of dendrites using a phase field model (context) - Wheeler, Murray et al. - 1993
8 Adaptive Finite Element Methods (context) - Eriksson, Estep et al.
8 A posteriori error bounds and global error control for appro.. (context) - Estep - 1995
7 An analysis of numerical approximations of metastable soluti.. (context) - Estep - 1994
5 Global error control for the continuous Galerkin finite elem.. - Estep, French - 1994
5 The effect of temperature-dependent viscosity on shear-flow .. (context) - Bertsch, Peletier et al. - 1991
4 Evolution g'eometrique d'interfaces (context) - de Mottoni, Schatzmann - 1989
3 epidemic models with directed diffusion (context) - Meade, Milner - 1992
2 The dynamical behavior of the Galerkin method for ordinary d.. (context) - Estep, Stuart
2 The computability of the Lorenz system (context) - Estep, Johnson
2 An analysis of quadrature in Galerkin finite element methods.. (context) - Estep, Johnson
1 Voxel databases: A paradigm for parallel computing with mesh.. (context) - Williams - 1992
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