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Parallel Step Control

AUTHOR Feldman, Lev; Feldman Lev; Dmitrieva Olga et al.
PUBLISHER LAP Lambert Academic Publishing (04/29/2013)
PRODUCT TYPE Paperback (Paperback)

Description
The work is devoted to the construction of efficient parallel algorithms of the integration step control in for simulation of dynamic objects. To select the optimum step size the paper proposes several parallel algorithms that are based on well-known, specially restructured methods of solving systems of ordinary differential equations. For these purposes, the parallel nested methods, explicit and implicit extrapolation schemes of variable order are used. As a criterion for the selection of the numerical scheme the inequalities which control accuracy and stability are used. When solving stiff problems, this allows at each step to select the optimum in terms of computational cost numerical scheme. Also the new difference block methods with the possibility of adapting the step, addressed at parallel implementation, are proposed. The basic idea, on which the design of block methods was based, is to obtain simultaneous approximations of the exact solution at points forming a block. On the basis of the proposed step size control algorithms test problems are implemented, the numerical solution of which provides the required accuracy with the maximum possible integration step.
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Product Details
ISBN-13: 9783659384257
ISBN-10: 3659384259
Binding: Paperback or Softback (Trade Paperback (Us))
Content Language: English
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Page Count: 72
Carton Quantity: 98
Product Dimensions: 6.00 x 0.17 x 9.00 inches
Weight: 0.26 pound(s)
Feature Codes: Illustrated
Country of Origin: US
Subject Information
BISAC Categories
Mathematics | General
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The work is devoted to the construction of efficient parallel algorithms of the integration step control in for simulation of dynamic objects. To select the optimum step size the paper proposes several parallel algorithms that are based on well-known, specially restructured methods of solving systems of ordinary differential equations. For these purposes, the parallel nested methods, explicit and implicit extrapolation schemes of variable order are used. As a criterion for the selection of the numerical scheme the inequalities which control accuracy and stability are used. When solving stiff problems, this allows at each step to select the optimum in terms of computational cost numerical scheme. Also the new difference block methods with the possibility of adapting the step, addressed at parallel implementation, are proposed. The basic idea, on which the design of block methods was based, is to obtain simultaneous approximations of the exact solution at points forming a block. On the basis of the proposed step size control algorithms test problems are implemented, the numerical solution of which provides the required accuracy with the maximum possible integration step.
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