I'm writing a paper, please can you tell me which sentence is the right?
The Pseudo-code is outlined in Fig 2 and we elaborate it in the following section.
The Pseudo-code is outlined in Fig 2 and we elaborate on it in the following section.
As @Andrew Leach mentions in his comment, it depends on what you want to say. Merriam-Webster online has a definition that takes account of the distinction between the transitive and intransitive forms.
I should take this to mean that in the subsequent section the Pseudo-code itself appears, fleshed out, worked out, given in full detail.
This I should understand as meaning that in the subsequent section the Pseudo-code is explained in much greater detail.