A Reproducing Kernel Hilbert Discretization Method for Linear PDEs with Nonlinear Right-hand Side

Abstract

We present a scheme to extend the method Aveiro Dis-cretization Method in Mathematics (ADMM) to linear PDEs where the right-hand side may (nonlinearly) depends on u. Then, we apply the scheme to find the (optimal) discretization solution of a problem involving a general second order differential operator with arbitrary coefficient functions and a cubic nonlinearity.