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.
- 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
L. S. Jacobsen and R. S. Ayre, Engineering vibrations, McGraw-Hill Book Co., Inc., New York, N. Y., 1958, pp. 244–259
L. S. Jacobsen, On a general method of solving second-order ordinary differential equations by phase-plane displacements, J. Appl. Mechanics 19, 543–553 (1952)
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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Article copyright:
© Copyright 1962
American Mathematical Society