Information Technology Reference
In-Depth Information
Dumping the solution array
u
to a file is performed by a
dump
method in a class
IO
:
class IO {
public static void dump (PrintStream f, double u[], double t0,
double dt)
{
int n = u.length;
double time = t0;
for(inti=0;i<n;i++){
f.println(time + " " + u[i]);
time += dt;
}
}
}
The main program can take this form:
class Demo {
public static void main (String argv[])
throws IOException
{
double tstop = Double.valueOf(argv[0]).doubleValue();
double dt = Double.valueOf(argv[1]).doubleValue();
int n = (int) (tstop/dt);
Func f = new f1();
double u0 = 1.0;
double u [] = Heun.advance (f, u0, dt, n);
double error = u[n] - Math.exp(-dt
*
n);
System.out.println("end value=" + u[n] + " error=" + error);
PrintStream file = new PrintStream(new FileOutputStream
("sol.dat"));
IO.dump (file, u, 0.0, dt);
file.close();
}
}
Plotting of the solution is subjected to the same comments as we made for C
CC
:
Calling a Java plotting library is possible, but there are no standard plotting tools to
be used.
6.4.6
Matlab
In Matlab, we implement Algorithm
6.12
as a function
heun
in an M-file
heum.m
:
function u = heun (f, u0, dt, n)
% HEUN numerical integration of ODEs by Heun's method
f = fcnchk(f);
u = zeros(n+1,1); % make n+1 zeros (as initialization)
% initial condition:
u(1) = u0;
% advance n steps:
for i = 1:n % i <-> i-1 compared to the original algorithm
v = feval(f, u(i));
u(i+1) = u(i) + 0.5
*
dt
*
(v + feval(f, u(i) + dt
*
v));
%fprintf('u(%d)=%g\n',i+1,u(i+1))
end
As in Java, it is convenient to create arrays wherever we need them and return them
from functions, if desired. Matlab will automatically delete arrays when they are no
