euler.rar

# include <stdio.h> # include <stdlib.h> # include <time.h> # include "euler.h" /******************************************************************************/ void euler ( void dydt ( double x, double y[], double yp[] ), double tspan[2], double y0[], int n, int m, double t[], double y[] ) /******************************************************************************/ /* Purpose: euler approximates the solution to an ODE using Euler's method. Licensing: This code is distributed under the GNU LGPL license. Modified: 25 April 2020 Author: John Burkardt Input: dydt: a function that evaluates the right hand side of the ODE. double tspan[2]: contains the initial and final times. double y0[m]: a column vector containing the initial condition. int n: the number of steps to take. int m: the number of variables. Output: double t[n+1], y[m*(n+1)]: the times and solution values. */ { double dt; double *dy; int i; int j; double tfirst; double tlast; dy = ( double * ) malloc ( m * sizeof ( double ) ); tfirst = tspan[0]; tlast = tspan[1]; dt = ( tlast - tfirst ) / ( double ) ( n ); j = 0; t[j] = tspan[0]; for ( i = 0; i < m; i++ ) { y[i+j*m] = y0[i]; } for ( j = 0; j < n; j++ ) { dydt ( t[j], y+j*m, dy ); t[j+1] = t[j] + dt; for ( i = 0; i < m; i++ ) { y[i+(j+1)*m] = y[i+j*m] + dt * dy[i]; } } free ( dy ); return; } /******************************************************************************/ void timestamp ( ) /******************************************************************************/ /* Purpose: timestamp prints the current YMDHMS date as a time stamp. Example: 17 June 2014 09:45:54 AM Licensing: This code is distributed under the GNU LGPL license. Modified: 17 June 2014 Author: John Burkardt */ { # define TIME_SIZE 40 static char time_buffer[TIME_SIZE]; const struct tm *tm; time_t now; now = time ( NULL ); tm = localtime ( &now ); strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm ); printf ( "%s\n", time_buffer ); return; # undef TIME_SIZE }