Consider the one dimensional heat equation u t = 2 2u x2 , 0 x L, 0 t T, that describes the evolution of temperature u(x, t) along a bar of length L, as a function of the position x and time t. Here denotes the thermal diffusivity of the material. Let us assume the following boundary conditions:

Problem 2 Numerical Differentiation (2+2)+4+4+4+(1+3) = 20 points) Consider the one dimensional heat equation Dua OSISL. OSTST. that describes the evolution of temperature (I. t) along a bar of length L, as a function of the position I and time t. Here a denotes the thermal diffusivity of the material. I following boundary conditions: (0.t) = (L. t) = 0 for 0