Approximate solution (with error bounds) to a nonlinear, nonautonomous second-order differential equation

✍ Scribed by James G. Taylor

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 851 KB
• Volume: 306
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(78)90084-4

✦ Synopsis

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.