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A Reproducing Kernel Hilbert Discretization Method for Linear PDEs with Nonlinear Right-hand Side
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.
Reproducing kernel Hilbert spaces, Tikhonov regularization, discretization solution, partial differential equation