APPROXIMATE SOLUTIONS OF A NON-LINEAR DIFFERENTIAL EQUATION USING LAPLACE-TRANSFORM AND REVERSION-OF-SERIES TECHNIQUES.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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The reversion-of-series method is extended to the s - domain by using non-linear Laplace transforms. The reversion of series in the s - domain is applied to a non-linear differential equation and approximate solutions are obtained. The approximate solution is modified for the case where the steady state is a constant value by calculating the exact steady-state value and applying it to the reversion approximation. The non-linear differential equation considered is Duffings equation with a damping term and sinusoidal and constant forcing functions. The theoretical solutions are compared to machine solutions. Author
- Numerical Mathematics