Solution of Nonlinear Differential Equations by the Reversion Method

Abstract

By the use of the reversion method certain types of ordinary nonlinear differential equations can be reduced to a set of ordinary linear differential equations which may conveniently be solved by the Laplace transform. The expression for the general member of the linear set is developed and written out in detail for certain illustrative terms. The method is applied to two simple problems for which the answers are exactly known so that some idea may be obtained as to the excellence of the approximations supplied by this method.

Some Aspects of the Measurement of Oscillatory Hydraulic Flow Including Nonlinear Effects

“…• [18] from Equation [8]. The solution for /JL (the fractional deviation of u 2 from u 2 , s.s.) is (to the same order as Equation [11 ]) written where Ai = tan -1 -(Jco/2) and A 2 = tan -1 -JOJ. Three facts are at once apparent from Equation [19].…”

“…It should be noted that in deriving Equation [11] two important assumptions have been made. First, the inertia of the fluid in the meter was neglected; second, the flow coefficient K was assumed to be constant.…”

“…In other words, Equation [11 ] expresses the error in using the flow rate u 2 , s.s. calculated from the mean pressure drop Ap.…”

“…This equation is nonlinear, but a series solution can be obtained using the reversion method of solution (10,11,12). The method of solution is outlined in Appendix B.…”

Schaltvorg�nge in Gleichstromkreisen mit nichtlinearem Widerstand und nichtlinearer Induktivit�t

“…So kann man z. B. viele derartige Gleichungen durch gewisse L6sungsansiitze in Systeme yon unendlich vielen line ar en Differentialgleichungen fiberfiihren (Reversions-oder Umkehrverfahren [5], [6]). Ferner kommt dem Verfahren der sog.…”