If the president says, "everything in the war is going as planned. trust me, i am the president," he is using what form of the elaboration likelihood model? under-route processing peripheral-route processing central-route processing classic-route processing

The president is using the peripheral-route processing form of the elaboration likelihood model.
It means that the listener will decide whether or not to believe in something based on the attractiveness of the speaker/his words, and not the message itself. So, they won't really pay much attention to what the president actually said, but given that he is the president, the listeners may choose to believe him solely because of that fact.