Extended power series solution for Perkins-Kern-Nordgren model of hydraulic fracture

The extended Power Series (XPS) method can be extremely useful for solving nonlinear equations with regular and irregular singular points. The extended power series is considered times a logarithm or times a fractional power of ζ , etc.). This research shows it is simple to solve approximately the Perkins-Kern-Nordgren (PKN) model of hydraulic fracture. To illustrate the effectiveness and convenience of the XPS method, we consider the two cases of dimensionless PKN equation containing the M-scaling and M ̃-scaling. The results compared with available analytical results verified excellent agreements.