Name
Abstract | ||
|---|---|---|
Shooting, finite difference or Harmonic Balance techniques in conjunction with Newton's method are widely employed for the numerical calculation of limit cycles of oscillators. The resulting set of nonlinear equations are normally solved by damped Newton's method. In some cases however divergence occurs when the initial estimate of the solution is not close enough to the exact one. A two-dimensional homotopy method is presented in this paper which overcomes this problem. The resulting linear set of equations employing Newton's method is under-determined and is solved in a least squares sense for which a rigorous mathematical basis can be derived |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1109/DATE.2002.998497 | Paris |
Keywords | Field | DocType |
Newton method,convergence of numerical methods,finite difference methods,least squares approximations,limit cycles,oscillators,Newton method,continuation method,convergence,damped Newton method,finite difference technique,harmonic balance technique,least squares method,limit cycle,linear equation,nonlinear equation,numerical method,oscillator,shooting technique,steady-state characteristics,two-dimensional homotopy | Least squares,Applied mathematics,Mathematical optimization,Newton fractal,Nonlinear system,Finite difference,Computer science,Parallel computing,Finite difference method,Local convergence,Harmonic balance,Newton's method | Conference |
ISSN | ISBN | Citations |
1530-1591 | 0-7695-1471-5 | 3 |
PageRank | References | Authors |
0.73 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hans Georg Brachtendorf | 1 | 13 | 7.00 |
| Lampe, S. | 2 | 3 | 0.73 |
| Rainer Laur | 3 | 241 | 35.65 |
| Melville, R. | 4 | 3 | 0.73 |