A very thick wall with constant thermal diffusivity a and a constant initial temperature ϑ0 is heated at its surface. The temperature rises there, between t = 0 and t = t∗ linearly with time t, to the...

A very thick wall with constant thermal diffusivity a and a constant initial temperature ϑ0 is heated at its surface. The temperature rises there, between t = 0 and t = t∗ linearly with time t, to the value ϑ₁
> ϑ₀, which remains constant for t>t∗. The temperature profile in the wall at times t = t∗ and t = 2 t∗ is to be calculated numerically. The simple explicit difference method is to be used, with ∆t = t∗/6 and M = 1/3, and the normalised temperature ϑ⁺
= (ϑ − ϑ0)/(ϑ₁
− ϑ₀) is to be used. Compare the numerically calculated values with the exact solution