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Methods of Small Parameter in Mathematical Biology (Hardcover, 2014)
Loot Price: R3,419
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Methods of Small Parameter in Mathematical Biology (Hardcover, 2014)
Series: Modeling and Simulation in Science, Engineering and Technology
Expected to ship within 12 - 17 working days
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This monograph presents new tools for modeling multiscale
biological processes. Natural processes are usually driven by
mechanisms widely differing from each other in the time or space
scale at which they operate and thus should be described by
appropriate multiscale models. However, looking at all such scales
simultaneously is often infeasible, costly, and provides
information that is redundant for a particular application. Hence,
there has been a growing interest in providing a more focused
description of multiscale processes by aggregating variables in a
way that is relevant to the purpose at hand and preserves the
salient features of the dynamics. Many ad hoc methods have been
devised, and the aim of this book is to present a systematic way of
deriving the so-called limit equations for such aggregated
variables and ensuring that the coefficients of these equations
encapsulate the relevant information from the discarded levels of
description. Since any approximation is only valid if an estimate
of the incurred error is available, the tools the authors describe
allow for proving that the solutions to the original multiscale
family of equations converge to the solution of the limit equation
if the relevant parameter converges to its critical value. The
chapters are arranged according to the mathematical complexity of
the analysis, from systems of ordinary linear differential
equations, through nonlinear ordinary differential equations, to
linear and nonlinear partial differential equations. Many chapters
begin with a survey of mathematical techniques needed for the
analysis. All problems discussed in this book belong to the class
of singularly perturbed problems; that is, problems in which the
structure of the limit equation is significantly different from
that of the multiscale model. Such problems appear in all areas of
science and can be attacked using many techniques. Methods of Small
Parameter in Mathematical Biology will appeal to senior
undergraduate and graduate students in applied and biomathematics,
as well as researchers specializing in differential equations and
asymptotic analysis.
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