A GEOMETRIC APPROACH TO BURGERS' RICCATI EQUATION.

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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 Riccatis Equation is included. Author

Author(s):
Gallagher, Gerald Lee
Author Organization(s):
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
Descriptive Note:
Master's thesis,
Pagination:
0056

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
(*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, TURBULENCE), HYPERGEOMETRIC FUNCTIONS, SPECIAL FUNCTIONS(MATHEMATICAL), POLYNOMIALS, THESES
Field(s)/Group(s):
Numerical Mathematics
Keyword(s):
BURGERS EQUATION, *RICCATI EQUATION, HERMITE FUNCTIONS
Report Date:
1970 Jun 01