I need to create matrix without using loops

Topic : Numerical Differentiation Using Matlab

Below is given table for the time t and its corresponding x position

Use forward and central differential scheme to compute velocity and acceleration by constructing differential matrix for the first derivative and multiplying the matrix and vectors (not allowed to use loop) as it is matrix based calculation.

Forward differential scheme is = x(i+1)-x(i) / t(i+1)-t(i)

***Expecting to use Sparse*** However open to use for other function as well

Please note end position is same as start position hence velocity should be equal for t1 and t10 (Please provide just Matlab Code for this)

Time t = 0 0.0775 0.2346 0.3015 0.3682 0.4345 0.5006 0.5665 0.6321 0.6974

X position 3.1909 3.1818 3.1547 3.1104 -0.0499 -0.0499 3.1104 3.1547 3.1818 3.1909

[Prabha Bhandari]

I just want to know the matrix formation code for forward and central differentation for function of 2 Phi

Answer 1

[KSSV]

Read about the function diff, gradient.