how to convert baking time to a smaller pan

I have a cheesecake recipe that is baked in a 9" spring form pan I would like to know how to convert the baking time to a 4 1/2" spring form pan. The original recipe cooks for 10 minutes at 400 the the oven is turned down to 200 and baked for 45 more minutes then the cheesecake is left in the oven with the oven door slightly open for 3 more hours any suggestions..

You may want to cut out the 10 minutes at 400 degrees and just bake at 200 degrees for about 45 minutes and check to see if it's almost set. If not, keep in the oven and check every 5 minutes until it's almost wet.

I hope this helps and good luck!