# discretization of variable parameters

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 June 21, 2011, 17:42 discretization of variable parameters #1 New Member   Join Date: May 2009 Posts: 6 Rep Power: 17 Dear all, in a porous layer I have a certain liquid s(x) distribution. The relative permeability is function of it: k(x) = s(x)^3. I need to determine the derivative of k, dk/dx. Should I discretize k: dk/dx|i = (k(i+1) - k(i-1))/(2h) or reduce the derivative as follow: dk/dx|i = 3*s(i)^2 * ds/dx|i = 3*s(i)^2*((s(i+1) - s(i-1))/(2h)) ? They lead to different results, and can not find a valid reason to choose one of them. thanks and regards Mauri

 June 25, 2011, 16:44 #2 Senior Member     p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19 Dear friends: The difference come from the discretisation error.for example, if we set s(x)=x; x|i=0.1; then dk/dx|i=(x+h)^3-(x-h)^3/(2*h); using the reduced form we have dk/dx|i=3*x^2*ds/dx=3*x^2; if we set h=0.1, the first one gives a value of 0.40 while the second one gives 0.030. if we reduce the h to 0.01, then the first one gives a avalue of 0.0301;

 Tags derivatives, discretization, parameter