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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Random Ordinary Differential Equations and Their Numerical Solution (Paperback, Softcover reprint of the original 1st ed. 2017)
Loot Price: R3,988
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Random Ordinary Differential Equations and Their Numerical Solution (Paperback, Softcover reprint of the original 1st ed. 2017)
Series: Probability Theory and Stochastic Modelling, 85
Expected to ship within 10 - 15 working days
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This book is intended to make recent results on the derivation of
higher order numerical schemes for random ordinary differential
equations (RODEs) available to a broader readership, and to
familiarize readers with RODEs themselves as well as the closely
associated theory of random dynamical systems. In addition, it
demonstrates how RODEs are being used in the biological sciences,
where non-Gaussian and bounded noise are often more realistic than
the Gaussian white noise in stochastic differential equations
(SODEs). RODEs are used in many important applications and play a
fundamental role in the theory of random dynamical systems. They
can be analyzed pathwise with deterministic calculus, but require
further treatment beyond that of classical ODE theory due to the
lack of smoothness in their time variable. Although classical
numerical schemes for ODEs can be used pathwise for RODEs, they
rarely attain their traditional order since the solutions of RODEs
do not have sufficient smoothness to have Taylor expansions in the
usual sense. However, Taylor-like expansions can be derived for
RODEs using an iterated application of the appropriate chain rule
in integral form, and represent the starting point for the
systematic derivation of consistent higher order numerical schemes
for RODEs. The book is directed at a wide range of readers in
applied and computational mathematics and related areas as well as
readers who are interested in the applications of mathematical
models involving random effects, in particular in the biological
sciences.The level of this book is suitable for graduate students
in applied mathematics and related areas, computational sciences
and systems biology. A basic knowledge of ordinary differential
equations and numerical analysis is required.
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