Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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An optimization of the phase-plane-delta method for the solution of non-linear differential equations


Authors: Carl A. Ludeke and Richard R. Weber
Journal: Quart. Appl. Math. 20 (1962), 67-77
MSC: Primary 34.40
DOI: https://doi.org/10.1090/qam/137890
MathSciNet review: 137890
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Abstract: An improvement to the phase-plane-data method of solving non-linear differential equations of the type $ {d^2}x/d{t^2} + H\left( x \right) = 0$ is discussed. This improvement provides a means of determining an optimized value of the parameter $ p$, frequency. In the conventional phase-plane-delta method the parameter $ p$ is chosen either arbitrarily or as the coefficient of the positive linear term. The phase-plane trajectory and period of oscillation can be more readily determined by this method than by the conventional phase-plane-delta method.


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

  • [1] L. S. Jacobsen, On a general method of solving second-order ordinary differential equations by phase-plane displacements, J. Appl. Mech. 19 (1952), 543–553. MR 0051586
  • [2] L. S. Jacobsen and R. S. Ayre, Engineering vibrations, McGraw-Hill Book Co., Inc., New York, N. Y., 1958, pp. 244-259

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DOI: https://doi.org/10.1090/qam/137890
Article copyright: © Copyright 1962 American Mathematical Society


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