Modeling and Simulation in Science, Engineering and Technology

Methods of Small Parameter in Mathematical Biology

Authors: Banasiak, Jacek, Lachowicz, Mirosław

  • Unified approach to singular perturbed problems
  • Applications and examples to mathematical biology
  • Chapters are arranged according to the mathematical complexity
see more benefits

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-05140-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-05139-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-319-38183-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

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.

Table of contents (9 chapters)

  • Small Parameter Methods: Basic Ideas

    Banasiak, Jacek (et al.)

    Pages 1-44

  • Introduction to the Chapman–Enskog Method: Linear Models with Migrations

    Banasiak, Jacek (et al.)

    Pages 45-76

  • Tikhonov–Vasilyeva Theory

    Banasiak, Jacek (et al.)

    Pages 77-104

  • The Tikhonov Theorem in Some Models of Mathematical Biosciences

    Banasiak, Jacek (et al.)

    Pages 105-141

  • Asymptotic Expansion Method in a Singularly Perturbed McKendrick Problem

    Banasiak, Jacek (et al.)

    Pages 143-172

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-05140-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-05139-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-319-38183-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Methods of Small Parameter in Mathematical Biology
Authors
Series Title
Modeling and Simulation in Science, Engineering and Technology
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-05140-6
DOI
10.1007/978-3-319-05140-6
Hardcover ISBN
978-3-319-05139-0
Softcover ISBN
978-3-319-38183-1
Series ISSN
2164-3679
Edition Number
1
Number of Pages
XI, 285
Number of Illustrations and Tables
8 b/w illustrations, 9 illustrations in colour
Topics