There are many ways to improve your speed over the 100 meters or 200m sprints. Essentially if you improve your 100m time by 1 second for example you could expect to improve your 200m time by 2 seconds with the right training
One way that worked well for me allowing me to better my 100m time by 1.3 sec and 200m time by 2 sec was to intensify with weight training (do squats, dead-lifts and bench press: 2x8-12 for start as, and try to improve your weights), develop your primary acceleration on the track by sprinting 30 meters first before running out in distance.
This can be done by doing quality repetitions maybe 2X3 lots of 30 meter sprints with at least 4 min rest between reps and 10 minutes between sets. As you get stronger with your weights you will get faster at your acceleration- get some one to time your 30m sprints you should expect improvements in 8 weeks time after doing both track and weight training on the same day, but training done every second day.
After 8 weeks you could start going out in distance try 40m- 60m (always do track first) you could drop your repetitions on your exercises so maybe 2x6 reps or 2x 5 reps on squats dead-lifts and bench press, but your weights should be constantly going up
On alternate days when not doing track and weight work you could go for a light jog for recovery, or do interval runs like 10 x100 meters, but must be done at 70 % of your best 100m time or 200m time respectively (ie 5 x200 meters done at 70% of your best 200m time of 30 sec is 42 seconds. So your 10x100m may be done at 20 seconds each or 70% of your best 100m time.
I hope this helps for more information have a look at charliefrancis.com (ben johnsons coach) join the forum its free it has helped me heaps