Discretize the nonlinear Hammerstein operator

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I would like to know please how to discretize the following special instance of nonlinear Hammerstein operator (in matlab if it is possible):

$F : H^{1}[0,1] \rightarrow L^{2}[0,1],$

$ F(x)(s):=\int_{0}^s x(t)^{3}dt$

Thank you for your help !