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Classical seventh-, sixth-, and fifth-order runge-kutta-nystrom formulas with stepsize control for general second-order differential equations
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Fehlberg, E. |
| Copyright Year | 1974 |
| Description | Runge-Kutta-Nystrom formulas of the seventh, sixth, and fifth order were derived for the general second order (vector) differential equation written as the second derivative of x = f(t, x, the first derivative of x). The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the local truncation error in x, and they require no more evaluations per step than the earlier Runge-Kutta formulas for the first derivative of x = f(t, x). The developed formulas are expected to be time saving in comparison to the Runge-Kutta formulas for first-order differential equations, since it is not necessary to convert the second-order differential equations into twice as many first-order differential equations. The examples shown saved from 25 percent to 60 percent more computer time than the earlier formulas for first-order differential equations, and are comparable in accuracy. |
| File Size | 2234893 |
| Page Count | 89 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19740026877 |
| Archival Resource Key | ark:/13960/t5bc8r88n |
| Language | English |
| Publisher Date | 1974-10-01 |
| Access Restriction | Open |
| Subject Keyword | Accuracy Numerical Analysis Vector Analysis Differential Equations Runge-kutta Method Truncation Errors Step Functions Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
