Publication Cover
Applicable Analysis
An International Journal
Volume 26, 1987 - Issue 2
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Original Articles

A note on the proper choice of scales in two variable expansions

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Pages 161-176 | Received 27 Mar 1987, Published online: 02 May 2007

References

  • Cole , J. D. and Kevorkian , J. Uniformly valid asymptotic approximations for certain non-linear differential equations . Proc. Internat. Sympos. Non-linear Differential Equations and Non-linear Mechanics . pp. 113 – 120 . New York : Academic Press .
  • Kevorkian , J. 1966 . “ The two uariable expansion -procedure for the approximate solution of certain nonlinear differential equations ” . In Lectures in Applied Mathematics,Space Mathematics , Edited by: Rosser , J. W. Vol. 7 , 206 – 275 . Providence, RI : American Mathematical Society .
  • Kevorkian , J. and Cole , J. D. 1981 . “ Ferturbation Kethods in Applied Mathematics ” . In Applied Mathematical Sciences , Vol. 34 , New York : Springer . ch. 3
  • Nayfeh , A. H. 1973 . Perturbation Methods , New York : Wiley . ch. 6
  • Morrison , J. A. 1966 . Comparison of the modified method of averaging and the two uariable expansion procedure . SIAM Rev , 8 : 66 – 85 .
  • Reiss , E. L. 1971 . On multiuariable expansions . SIAM Rev , 13 : 189 – 191 .
  • Kollett , F. W. 1974 . Two-timing methods valid on expanding interuals . Siam J. Math. Anal , 5 : 613 – 625 .
  • Greenlee , W. M. and Snow , R. E. 1975 . Two-Timing on the Half Line for Damped Oscillator Equations . J. Math. Anal. Appl , 51 : 394 – 428 .
  • Kamke , E. 1969 . Differentialgleichungen , Vol. I , 143 – 145 . Leipzig : Akademische Verlags-gesellschaft .

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