Asymptotics of Slow-time Processes, First Steps

  • Jan A. Sanders
  • Ferdinand Verhulst
Part of the Applied Mathematical Sciences book series (AMS, volume 59)


In this chapter we shall discuss those concepts and elementary methods in asymptotics which are necessary prerequisites for the study of slow-time processes in nonlinear oscillations. In considering a function defined by an integral or defined as the solution of a differential equation with boundary or initial conditions, approximation techniques can be useful. In the applied mathematics literature no single theory dominates but many techniques can be found based on a great variety of concepts leading in general to different results. We mention here the methods of numerical analysis, approximation by orthonormal function series in a Hilbert space, approximation by convergent series and the theory of asymptotic approximations. Each of these methods can be suitable to understand an explicitly given problem. In this book we consider problems where the theory of asymptotic approximations is useful and we introduce the necessary concepts in detail.


Periodic Solution Standard Form Nonlinear Oscillation Asymptotic Approximation Order Function 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Jan A. Sanders
    • 1
  • Ferdinand Verhulst
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.Mathematical InstituteState University of UtrechtUtrechtThe Netherlands

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