Polynomial Approximate Solutions of an Unconfined Forchheimer Groundwater Flow Equation

•Approximate analytical solutions to the Forchheimer equation for four types of the boundary conditions (power-law head, exponential head, power-law flux and exponential flux) were constructed.•Effective numerical procedure based on the Shampines rescaling method is introduced for the solution of the Forchheimer equation.•Approximate solutions replicate known exact solutions.