Accession Number : ADP002958

Title :   A Finite Integral Transform (FIT) Method for Differential Equations Having Asymptotic Solutions,


Personal Author(s) : Daly,C. J.

Report Date : FEB 1984

Pagination or Media Count : 8

Abstract : An analytical method is developed for differential equations whose solutions y(t) decay asymptotically for large t. The approach, called the finite integral transform (FIT) method, is based upon the use of selected transform-inverse pairs for which the inverses are known explicitly. Using the method, approximate analytical expressions for y(t) are obtained in the form of series of orthogonal functions psi sub n (t). Asymptotic behavior of the approximating series is guaranteed by requiring each psi sub n t be asymptotic for large t. The central feature of the FIT approach is the generation of a system of algebraic equations which is solved for the vector of coefficients appearing in the orthogonal series solution. The FIT method amounts to a discretization of the unknown solution in a frequency domain. This is in contrast to finite difference and finite element methods which discretize over the domain of independent variables. The FIT approach is demonstrated by application to a simple linear ODE with variable coefficient. (Author)

Descriptors :   *Integral transforms, Asymptotic series, Orthogonality, Linear differential equations, Coefficients, Variables, Approximation(Mathematics)

Distribution Statement : APPROVED FOR PUBLIC RELEASE