ERROR BOUNDS FOR QUASI-HARMONIC OSCILLATIONS: NON-RESONANT CASE.
Abstract
The report describes a functional equation method for estimating the convergence interval and truncation error for periodic series solutions when the differential equation is a scalar, quasiharmonic equation of the non-resonant type. The method is due originally to A. M. Lyapunov, has been recently discussed in the Soviet Union by Yu. A. Ryabov particularly in connection with the convergence interval problem, and was described in a previous report in application to vector quasilinear equations. Here for the scalar, quasiharmonic, non-resonant case, the report gives a concise derivation, construction procedure, and solution method for a pair of functional algebraic equations whose solution majorizes the error in the differential equation truncated solution for parameter values within the convergence interval. The parameter value for which the functional equations first cease to have a solution provides an estimate of the convergence interval, and can be calculated explicitly. The report concludes by calculating the errors in zero-order and first-order solutions of the forced Duffing equation (non-resonant case). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1967
- Accession Number
- AD0666306
Entities
People
- Robert J. Mclaughlin
Organizations
- Harvard University