https://animetosho.org/about

HJSplit is your tool.

The easiest method is to download the program hjsplit @ http://www.hjsplit.org/
Choose the proper version you need near the bottom of the page.
Download it, (extract it if you have the windows one).
Run hjsplit.exe
Once the program opens, you should have 6 options.
Choose Join
Now a new pop-up windows open.
Click on Input file
Go to the proper file destination (such as your downloads folder, if you're not already there)
Now there should only be one file to choose from (or other folders)
Named unico_-_the_island_of_magic_(sanrio_co.,_ltd.-tezuka_pro,_1983).mkv.001 or similar file ending in .mkv.001
Click Open.
Now the pop-up menu should display the input file and the output file(and you will see that it ends with .mkv not .mkv.001 or anything)
Now all you have to do is click start.
Once it finishes (and tells you), you should have the complete file. Huzzah!
Now you can play the video.

If that doesn't come clear, here is a youtube clip: http://www.youtube.com/watch?v=CrCurzfT4IM

Another program that will get the job done is filejoiner @ http://www.igorware.com/file-joiner
This will feature similar steps.

Lastly there is another options, if you're up to the task.
open up the command prompt (win+R then type cmd.exe)
move to the directory containing the split files (use cd) - or move the files to the user root folder.
then type
COPY /B <source file1>+<source file2>+<source file3>+.... <destination file>
where <source file1> is .mkv.001  and <source file2> is .002 and so on. and <destination file> is the file ending in .mkv.
This is easier done if you rename the parts before hand to avoid unnecessarily typing/mistakes. do A.mkv.001 B.mkv.002 ....

After executing the command windows should give you the complete file with no issues during opening/playback.

For linux:

cat file1 file2 > file3