Runge-Kutta method: Difference between revisions
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=={{header|Perl}}==
There are many ways of doing this. Here we define the runge_kutta function
as a function of <math>y'</math> and <math>\delta t</math>, returning a closure
which itself takes <math>(t, y)</math> as argument and returns the next <math>(t, y)</math>.
Notice how we have use sprintf to deal with floating point rounding. See perlfaq4.
<lang perl>sub runge_kutta {
my ($yp
sub {
my @dy = $dt * $yp->( $t , $y );
push @dy, $dt * $yp->( $t + $dt/2, $y + $dy[0]/2 );
push @dy, $dt * $yp->( $t + $dt/2, $y + $dy[1]/2 );
push @dy, $dt * $yp->( $t +
return $t + $dt, $y +
}
}
▲my $t = 0;
▲my $RK = runge_kutta sub { $_[0] * sqrt $_[1] }, 0, 1, .1;
for(
($t, $y) = $RK->($t, $y)
) {
printf "y(%2.0f) = %12f ± %e\n", $t, $y, abs($y - ($t**2 + 4)**2 / 16)
if sprintf("%.4f", $t) =~ /0000$/;
}</lang>
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