MATLAB: How can I solve this partial derivatives

#fick's lawdiffusion in a cylindrical membrane

dc/dz = (a/x * dc/dx +a*d^2c/dx^2) /(1-x^2/L) where a,L are constant.

Use pdepe.

Best wishes

Torsten.

By integrating both sides of the equation:

integral_{y=y0}^{y=y}y*(a-y) dy = (a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3)
integral_{x=x0}^{x=x}u/k dx = u/k*(x-x0)

Thus

(a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3) = u/k*(x-x0)

and the inverse function if the solution is given by

x = x0 + k/u*((a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3))

Best wishes

Torsten.

gradient uses central differences while diff(x) uses right-hand differences x(i+1)-x(i).