Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A new perturbation technique for differential equations with small parameters

Authors: M. A. Brull and A. I. Soler
Journal: Quart. Appl. Math. 24 (1966), 143-151
MSC: Primary 34.53
DOI: https://doi.org/10.1090/qam/208095
MathSciNet review: 208095
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Abstract: Ordinary linear differential equations containing small parameter $ \epsilon $ are investigated in regard to the existence of solutions in power series of the parameter. A new perturbation technique is developed which yields solutions more convenient for computation than comparable solutions obtained by making the usual series expansion in the small parameter. The new method is applied to second and fourth order differential equations in normal form and it is shown that the method yields asymptotic solution for small $ \epsilon $. Conditions needed for successful application of the method are discussed and a typical solution is obtained. Comparison of numerical results with an exact solution and with an ordinary perturbation solution indicates the usefulness of the technique.

References [Enhancements On Off] (What's this?)

  • [1] J. R. Vinson and M. A. Brull, New Techniques of Solutions for Problems in the Theory of Orthotropic Plates, Proc. 4th U. S. National Congress of Applied Mechanics, p. 817 (1962)
  • [2] A. I. Soler, Application of Perturbation Techniques to the Solution of Problems in Thermoviscoelasticity, Ph.D. Thesis, University of Pennsylvania, December, (1962)
  • [3] A. I. Soler and M. A. Brull, On the solution to transient coupled thermoelastic problems by perturbation techniques, Trans. ASME Ser. E. J. Appl. Mech. 32 (1965), 389–399. MR 0187511
  • [4] E. H. Mansfield, The Bending and Stretching of Plates, MacMillan, New York, p. 77 (1964)

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DOI: https://doi.org/10.1090/qam/208095
Article copyright: © Copyright 1966 American Mathematical Society

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