Newton's Method and Symmetry for Semilinear Elliptic PDE on the Cube

John M. Neuberger, Nandor Sieben, James W. Swift

We seek discrete approximations to solutions $u:\Omega \to R$ of semilinear elliptic partial differential equations of the form $\Delta u+f_s(u)=0$, where $f_s$ is a one-parameter family o…