Solve multiple integrals qith Newton-Cotes formulas

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Hi!! I'm trying to compute a biological model and one of the parts of it consists in a multiple integral function I am not being able to solve. I would highly appreciate if someone could guide me or help me in how to do it. The model equation is
Where pm= 0.06; Rmax = 70cm and u is the model function. I am not sure of how to solve it cause the general model includes the p function and the p function includes the u fuinction.
Thank you in advance
Torsten on 20 Mar 2022
If you don't have the complete u-vector available in each time step, you won't be able to solve the above equation.
It seems you have a 2d in space PDE (r and rho as independent variables). Did you plan to use MATLAB's PDE toolbox to solve ?

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