Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations
by S. S. Artemiev, T. A. Averina
ISBN 3111873161 (3-11-187316-1)
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Hardcover, Walter de Gruyter
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This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. The first chapter covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs). Here, general solutions of consistency equations are obtained, which lead to the construction of RTMs from the first to the fourth order. The second chapter deals with statistical simulation problems of the solution of the Cauchy problem for stochastic differential equation (SDE) systems. The mean-square convergence theorem is considered, as well as Taylor expansions of numerical solutions. Also included are applications of numerical methods of SDE solutions to partial differential equations and to analysis and synthesis problems of automated control of stochastic systems. The book should be of interest to specialists in the fields of computational mathematics and physics, probability theory and atuomated control theory. [via]
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