Diffusion forward and backward in time
ut = uxx, initial profile (1 − |x|)+: forward to t = 0.1, then backward. In each direction the red curve starts from the same data as the blue one plus ε sin nx.
ut = uxx, initial profile (1 − |x|)+: forward to t = 0.1, then backward. In each direction the red curve starts from the same data as the blue one plus ε sin nx.