Accession Number : AD0709925

Title :   A GEOMETRIC APPROACH TO BURGERS' RICCATI EQUATION.

Descriptive Note : Master's thesis,

Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s) : Gallagher,Gerald Lee

Report Date : JUN 1970

Pagination or Media Count : 56

Abstract : The directrix approach, which gives powerful insight to the geometric structure of solutions of the general Riccati equation, is developed. Burgers' Riccati equation is derived, and conclusions are drawn using the directrix approach concerning the boundedness properties of solutions of this equation with certain restrictions on parameter values. Closed form solutions are developed for Burgers' Riccati equation for certain parameter values. A method is produced to obtain the vertical assymptote for unbounded solutions of Burgers' Riccati equation with certain restrictions on parameter values. Conclusions drawn from the application of the directrix method to Burgers' equation are verified. A research bibliography for Riccati's Equation is included. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, TURBULENCE), HYPERGEOMETRIC FUNCTIONS, SPECIAL FUNCTIONS(MATHEMATICAL), POLYNOMIALS, THESES

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE