MATLAB: Ode45 versus quad/quadv/trapz

integrationode45quadtrapz

I have to compute the average of a given parameter, i.e. I have to solve an equation of the type
average_y(x) = A * integral( x^a * y * dx)
where a and A are constants and, as shown, y is a function of x. This equation can be written in the form
d/dx (average_y(x)) = A * x^a * y
What form can be better solved with Matlab? Should I use the first form (with trapz or quad for example)? Or the second form with an ode-function (like ode45)? Please tell me what function you would use regarding the method you choose.
Thanks for your help.
Tibo

Best Answer

Well, since you can't set a tolerance with trapz, the difference seems pretty clear there.
And if all you want is the final result, then why bother with an ode solver that will waste time in generating the intermediate results too?
So use the proper tool for the job. If you want to do numerical integration to compute an overall integral, as accurately as possible, use a tool designed to do just that. I have found quadgk to be more efficient and more robust than quad usually.
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