Parallel computations and numerical simulations for nonlinear systems of Volterra integro-differential equations

► We investigate systems of nonlinear Volterra integro-differential equations. ► We divide the systems into subsystems in such a way that each of them is solved by an independent processor. ► The results computed by the processors are shared only once in the process of computations. ► We solve the s...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 17; no. 7; pp. 3022 - 3030
Main Authors: Michaels, P., Zubik-Kowal, B.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2012
Subjects:
Computation
Computer simulation
Mathematical analysis
Mathematical models
Microprocessors
Nonlinear Volterra integro-differential equations
Nonlinearity
Numerical simulations
Parallel computing
Parallel processing
Run time (computers)
Thalamo-cortical systems
Nonlinear Volterra integro-differential equations
Parallel computing
Numerical simulations
Thalamo-cortical systems
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:► We investigate systems of nonlinear Volterra integro-differential equations. ► We divide the systems into subsystems in such a way that each of them is solved by an independent processor. ► The results computed by the processors are shared only once in the process of computations. ► We solve the subsystems concurrently in a parallel computing environment. ► The results of the numerical experiments show savings in the run time. We investigate thalamo-cortical systems that are modeled by nonlinear Volterra integro-differential equations of convolution type. We divide the systems into smaller subsystems in such a way that each of them is solved separately by a processor working independently of other processors results of which are shared only once in the process of computations. We solve the subsystems concurrently in a parallel computing environment and present results of numerical experiments, which show savings in the run time and therefore efficiency of our approach. For our numerical simulations, we apply different numbers np of processors and each case shows that the run time decreases with increasing np. The optimal speed-up is obtained with np=N, where N is the (moderate) number of equations in the thalamo-cortical model.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2011.11.006