This question has also been asked and answered here: Ritalin vs Adderall: What is the difference?
Adderall is newer than Ritalin, though not necissarily better or worse. Your doctor knows what he is doing regarding drug equivilancy, as 20mg of Adderall is just under the potency of 40mg of Ritalin. The comapritive breakdown (typical responses, not all people will react the same):
Ritalin: Intermediate length of action (4-6 hours)
Pros: More readily available (with the ADHD medication shortages of late), older and better studied long term, more stimulating than focusing (better for the ADD of old than the ADHD of modern terminology), better appetite than most stimulants allow for, cheapest of all stimulant ADHD meds.
Cons: Particular side effects are much worse than with other formulations, including headache, eye-strain (it seems), effects on blood pressure, and aggressive tenancies. Lower level of impulse control comparatively, more noticeable come-down, tolerance builds more rapidly.
Adderall: Low Intermediate length of action (4-5 hours)
Pros: A racemic mixture of three amphetamine salts and dextroamphetamine this purportedly extending length between initiation of dose and tolerance to it, both stimulating as well as focusing, most widely used ADHD medication to date allowing plenty of field observation, kicks in a little faster, slightly smoother come-down than older formulations
Cons: Major US shortages thanks to Shire's attempts at dominating with Vyvanse, second least expensive in immediate release form but priced beyond reason in XR form ($600 for 90 30mg caps at a pharmacy here in NC), more potential for addiction, tendency towards more false sense of well being and euphoria (some consider these "Pros"), may contain dyes which are very reactionary as far as allergic reactions are concerned
My 2 cents is that anyone will benefit more from Adderall over Ritalin in the short and long run. You may feel slightly more productive and if you focus will likely find it easier to maintain that focus. You may be a bit more jittery than you were on Ritalin, but at a dose as low as 20mg I doubt this will be much of an issue. If you can find the Adderall in stock at a local pharmacy and it's not exhausted of supply as it is here, you will most certainly enjoy the overall feeling of Adderall better than you did Ritalin. I'd recommend going to at least 30mg doctor permitting though, Adderall has a downside of causing irritation and difficulty concentrating at doses just at or below therapeutic levels, so too little can actually make your problems worse while on it (I take this from five or six personal anecdotal experiences with myself and others).
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