%0 eBook
%M Solr-EB000738832
%A Banasiak, Jacek
%I Springer International Publishing
%D 2014
%C Cham
%G English
%B Modeling and Simulation in Science, Engineering and Technology
%@ 9783319051406
%T Methods of Small Parameter in Mathematical Biology
%U https://doi.org/10.1007/978-3-319-05140-6?nosfx=y
%7 1st ed. 2014
%X Since any approximation is only valid if an estimate of the incurred error is available, the tools described 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.