Accession Number:

AD0607820

Title:

GALERKIN'S PROCEDURE FOR NONLINEAR PERIODIC SYSTEMS,

Descriptive Note:

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• Urabe,Minoru

Report Date:

1964-08-01

Pagination or Media Count:

85.0

Abstract:

It is shown that Galerkins procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution. This gives an explicit condition for applying Galerkins procedure and reveals the wide applicability of Galerkins procedure to general nonlinear periodic differential systems. The proof of this result is based on existence theorems which are derived from idea contained in Newtons iterative method. The relationship of Galerkins procedure to the method of averaging is also discussed. Finally the paper exemplifies Galerkins procedure with a certain nonlinear equation. Author

Descriptors:

• *NONLINEAR DIFFERENTIAL EQUATIONS
• *DIFFERENTIAL EQUATIONS
• NUMERICAL ANALYSIS
• NUMERICAL ANALYSIS
• NUMERICAL METHODS AND PROCEDURES
• BOUNDARY VALUE PROBLEMS
• OSCILLATION
• NONLINEAR SYSTEMS
• MAPPING(TRANSFORMATIONS)
• MATRICES(MATHEMATICS)
• POLYNOMIALS

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE