grep error ~/error/errorlog.txt >> ~/main/analysis.txt

$infile = 'errorlog.txt';
$outfile = 'analysys.txt';

open(INFILE,$infile) || die "Unable to Open $infile-$!";
open(OUTFILE,$outfile) || die "Unable to Open $outfile-$!";

while ( <INFILE> ) {
     print OUTFILE $_ if (/error/);
}

close INFILE;
close OUTFILE;

# Correction to my above post

$infile = 'errorlog.txt';
$outfile = 'analysys.txt';

open(INFILE,"$infile") || die "Unable to Open $infile-$!";
open(OUTFILE,">$outfile") || die "Unable to Open $outfile-
$!";

while ( <INFILE> ) {
     print OUTFILE $_ if (/error/);
}

close INFILE;
close OUTFILE;

We can do it in a simple way through command line with the
use of grep functionality without writing a program for that.

Suppose your log files(err.log, err_others.log, ......) are
present in "logs" folder.

1) Go to that path first 
2) logs]# grep -ir 'error' . > result.txt
   (-i for ignore case, -r for recursive search)
3) Observe that, it will grep all the places where ever
'error' is present and keep it in result.txt
4) If you just want the file names alone which contains 'error'
   logs]# grep -irl 'error' . > result.txt
   (-i for ignore case, -r for recursive search, 
    -l for listing the files)