Evening all,
I am attempting to solve a second order differential equation to get an equation of the substrate concentration as a function of r (i.e. S(r)). I have developed this equation, $\frac{d^2S}{dr^2}+\frac{2}{r}\frac{dS}{dr}-\frac{V_mS}{K+S}*\frac{1}{D}=0$, where $V_m, D, K$ are known values to me based on research and I also have two boundary conditions as it is a symmetrical spherical enzyme. Thus, $\frac{dS}{dr} = 0, r=0$ and $S=0.00001, R=0.001$ I am very new to Mathematica and have been attempting to solve this equation in the following manner:
DSolve[{S''[r] + (2/r)*S'[r] - (V*S[r])/(K + S[r])*1/D == 0, S'[0] == 0,
S[0.001] == 1.10*10^-4}, S[r], r]
I have not been successful in getting a solution as S(r) and am unsure where to begin on fixing the issue. Any help is greatly appreciated!
NDSolve
with explicit values for the parameters. But it seems you will need to move the initial point to something positive as it otherwise claimes a singularity at the origin. $\endgroup$ – Daniel Lichtblau Sep 17 '17 at 21:43