I am doing a problem that involve a PDE of d2u/dx^2=dx/dt with boundaries at 0 and 1 set to 0 and initial u at time = 0 set to 1. I have attached the problem as well as my solution to the problem which I believe to be right. The last part of the problem says "at short times, show that the solution reduces to the Error function solution. I know that the error function is defined as an integral of an exponential and that parseval's relations can be used to relate a sum to an integral. Is this how I should be approaching simplifying the answer for short times? If so, how might I start out relating the answer in terms of the Error function.


Parseval's Relation-parceval-s.png