Singular perturbation methods

  • J. D. Murray
Part of the Applied Mathematical Sciences book series (AMS, volume 48)


In §6.2 in the last chapter we briefly discussed, by way of example, some singular perturbation problems in linear differential equations which could be solved using the exponential method developed there. In this chapter we discuss some more generally applicable singular perturbation techniques. These are extremely powerful and let us consider nonlinear problems, involving a small or large parameter, with a view to extracting the principle features of the solutions which cannot be found by classical methods. A fundamental property of nonlinear problems that we shall be interested in is that the main features of the solutions are not contained in the linearized problem as we see in §7.2 below.


Singular Perturbation Secular Term Outer Solution Singular Perturbation Problem Matched Asymptotic Expansion 
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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • J. D. Murray
    • 1
  1. 1.Mathematics InstituteOxford UniversityOxfordEngland

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