# Recurrence Relation based on Vectors

I am new to Mathematica. I try to solve a recurrence relation based on vectors. So a[n] is a vector for all n (as well as b[n] and c[n]). The value for a[n] depends on the Euclidean norm of a[n-1] (see code below).

My code below, however, does not work. Do I have to tell Mathematica explicitly that I am working on vectors? How can I do this? Is Mathematica in general able to solve a recurrence like this?

 RSolve[{b[n] == 1/2 a[n - 1] + 1/2 c[n - 1],
a[n] == 1/(2*Norm[a[n - 1]])a[n-1] + 1/2 b[n - 1],
c[n] == 1/2 b[n - 1] + 1/(2 Norm[c[n - 1]]) c[n - 1]}, {a[n], b[n],
c[n]}, n]

• Knowing that a,b,c are vectors you could write a[n-1].a[n-1] instead of Norm[a[n-1]] . But the second and third equation might be inconsistent, because here you add scalar and vector on the right side. Oct 30 '18 at 10:50
• There was a missing factor after the first norm occurrence. I fixed this now. Oct 30 '18 at 10:56
• Consider doing it numerically. Oct 30 '18 at 11:49