Approximate solution (with error bounds) to a nonlinear,nonautonomous second-order differential equation |
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| Authors: | James G Taylor |
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| Institution: | Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, U.S.A. |
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| Abstract: | Two approximations are developed to the solution of an important nonlinear, nonautonomous second-order differential equation that arises in various fields of science and technology such as operations research, mathematical ecology and epidemiology. The origin of the second-order differential equation from a system of two nonlinear first-order differential equations modelling, for example, Lanchester-type combat between two homogeneous military forces is discussed. Extension of our results to a more general system of nonlinear first-order differential equations is indicated. Error bounds that do not require that the exact solution be known are developed. Some connections between our results and those for the Liouville-Green (or WKB) approximation to the solution of the linear second-order equation are indicated. |
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