How does one decide whether to compute an odd or an even extension of a function when solving an IBVP. For example:
Solve the following IBVP $$PDE : u_t(x, t) = 3u_{xx}(x, t) \text{ for } 0<x<2 \text{ and } t > 0$$ $$BC : u(0, t) = 0, u(2, t) = 0, t ≥ 0$$ $$IC : u(x, 0) = x^2 \text{ for } 0 ≤ x ≤ 2$$ The solution suggests computing an odd extension. Why an odd one and not an even extension I cannot understand. Thanks in advance for your help!