Abstract
The solution is obtained and validated by an existence and uniqueness theorem for the following nonlinear boundary value problem
ddx1+δy+γy2ndydx+2xdydx=0,x>0,y(0)=0,y(∞)=1,$$ \frac{d}{dx}\left[{\left(1+\delta y+\gamma {y}^2\right)}^n\frac{dy}{dx}\right]+2x\frac{dy}{dx}=0,x>0,y(0)=0,y\left(\infty \right)=1, $$
which was proposed in 1974 by Cho and Sunderland to represent a Stefan problem with a nonlinear temperature‐dependent thermal conductivity on the semi‐infinite line
(0,∞)$$ \left(0,\infty \right) $$. The modified error function of two parameters
φδ,γ$$ {\varphi}_{\delta, \gamma } $$ is introduced to represent the solution of the problem above, and some properties of the function are established. This generalizes the results obtained in earlier studies.