1.3 Homogeneous Heat PDE in 1D, Semi-infinite domain, No source. Laplace Transform method

  1.3.1 Left end at zero temperature, No source term, zero initial conditions
  1.3.2 Left end at temperature that depends on time. No source term, zero initial conditions

The following are analytical solutions to heat PDE in semi-infinite domain \(\left ( 0<x<\infty \right ) \). Laplace transform is used. For each case, the full analytical solution is given and compared to numerical solution in an animation.