I am trying to solve a one-dimensional heat equation problem with a piecewise continuous input of temperatures. Dr. Robert Lopez works through a solution of a nonhomogeneous boundary value problem using a sinusoidal equation for the temperature-time variation (Advanced Engineering Mathematics, Chapter 27, Section 27.2). I would like to develop the same solution using a temperature time history equation which consists of pairs of temperature-time points. Is there a way to define the time-history as one of the boundary equations? I was thinking of reading them from an array, but I would like the ability of evaluating the thermal gradient through the wall at any time point, not just the discrete values that are known.
Thank you for your assistance.