Accession Number : AD0664222

Title :   ERROR BOUNDS FOR QUASI-HARMONIC OSCILLATIONS: RESONANT CASE.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS

Personal Author(s) : McLaughlin,R. J.

Report Date : SEP 1967

Pagination or Media Count : 52

Abstract : The most common procedure for constructing the periodic solution of a quasilinear differential equation with periodic right-hand side usually involves an iterative procedure which theoretically yields the exact solution only after an infinite number of iterations, and provided that the perturbing parameter in the differential equation is sufficiently small. Such a procedure has the important practical defects that (1) the method usually gives no indication of how small the parameter must be for convergence to the true solution, and (2) the method usually gives little indication of how much error remains after the finite number of iterations with which one must be satisfied in any practical calculation. A previous report describes a functional equation method for estimating convergence intervals and truncation errors for the periodic series solutions of scalar, quasi-harmonic equations of the non-resonant type. The method is due originally to A. M. Lyapunov, and has been discussed primarily in connection with the convergence interval problem by Ryabov in the Soviet Union. The present report extends our previous discussion to the resonant case. The general form of the functional equations is derived for this case, and a practical construction procedure and solution method for the functional equations are given.

Descriptors :   (*DIFFERENTIAL EQUATIONS, PROBLEM SOLVING), TRANSCENDENTAL FUNCTIONS, NONLINEAR SYSTEMS, POLYNOMIALS, POWER SERIES, ITERATIONS, CONVERGENCE, RESONANCE, PERIODIC VARIATIONS, OSCILLATION, FUNCTIONAL ANALYSIS, PERTURBATION THEORY, NUMERICAL ANALYSIS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE