An iteration sequence based on the BLUES (beyond linear use of equation superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial differential equations. This extends previous work using this method for nonlinear ordinary differential equations with an external source term. Now. the initial condition plays the role of the source. https://www.roneverhart.com/Rawlings-34-Maple-Fungo-Bat-MLF6/