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NAMEode - numerical solution of ordinary differential equationsSYNOPSISode [ options ] [ file ]DESCRIPTIONode is a tool that solves, by numerical integration, the initial value problem for a specified system of first-order ordinary differential equations. Three distinct numerical integration schemes are available: Runge-Kutta-Fehlberg (the default), Adams-Moulton, and Euler. The Adams-Moulton and Runge-Kutta schemes are available with adaptive step size.The operation of ode is specified by a program, written in its input language. The program is simply a list of expressions for the derivatives of the variables to be integrated, together with some control statements. Some examples are given in the EXAMPLES section. ode reads the program from the specified file, or from standard input if no file name is given. If reading from standard input, ode will stop reading and exit when it sees a single period on a line by itself. At each time step, the values of variables specified in the program are written to standard output. So a table of values will be produced, with each column showing the evolution of a variable. If there are only two columns, the output can be piped to graph(1) or a similar plotting program. OPTIONSInput Options
Output Options
Integration Scheme OptionsThe following options specify the numerical integration scheme. Only one of the three basic options -R, -A, -E may be specified. The default is -R (Runge-Kutta-Fehlberg).
Error Bound Options
Informational Options
DIAGNOSTICSMostly self-explanatory. The biggest exception is `syntax error', meaning there is a grammatical error. Language error messages are of the formode: nnn: message...
where `nnn' is the number of the input line containing the error. If the -f option is used, the phrase "(file)" follows the `nnn' for errors encountered inside the file. Subsequently, when ode begins reading the standard input, line numbers start over from 1. No effort is made to recover successfully from syntactic errors in the input. However, there is a meager effort to resynchronize so more than one error can be found in one scan. Run-time errors elicit a message describing the problem, and the solution is abandoned. EXAMPLESThe programy' = y
y = 1 print t, y step 0, 1 solves an initial value problem whose solution is y=e^t. When ode runs this program, it will write two columns of numbers to standard output. Each line will show the value of the independent variable t, and the variable y, as t is stepped from 0 to 1. A more sophisticated example would be sine' = cosine
cosine' = -sine sine = 0 cosine = 1 print t, sine step 0, 2*PI This program solves an initial value problem for a system of two differential equations. The initial value problem turns out to define the sine and cosine functions. The program steps the system over a full period. AUTHORSode was written by Nicholas B. Tufillaro (nbt@reed.edu), and slightly enhanced by Robert S. Maier (rsm@math.arizona.edu) to merge it into the GNU plotting utilities.SEE ALSO"The GNU Plotting Utilities Manual".BUGSEmail bug reports to bug-gnu-utils@gnu.org.
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