# Manipulate plot of a system of PDEs with NDSolve

Modeling 1D diffusion of an enzyme, e, through a sphere with substrate, s, I arrive at the below equations:

I then pass these equations to NDSolve, Evaluate at a range of r and t and Plot and Manipulate as follows.

 Manipulate[
sol2 = NDSolve[{
tim] == (1/(k2/(k2 + k1r)))*(D0/((length^2) e0*k1f))*
(*initial conditions*)
(*boundary conditions*)
en[0, tim] == 1, sub[1, tim] == 1
}, {sub, en}, {rad, 0, r0}, {tim, 0, 10}];
Plot[Evaluate[
0, 1}, PlotRange -> All,
AxesLabel -> {"Front Position", "Concentration"},
PlotLegends -> {"substrate", "enzyme"}],
{{s0, 1}, 1, 10, 1},
{{k2, .5}, 0.1, 1},
{{k1r, 0.5}, 0.1, 1},
{{k1f, 1}, 1, 10, 1},
{{r0, 1}, 0, 1},
{{e0, 1}, 0.1, 1},
{{D0, .001}, 0.001, 1},
{{length, 1}, 1, 10},
{{beta, 1}, 0, 6}
]

• It looks like Toolbox is not compatible with version 12. – Alex Trounev May 2 at 11:12
• The code contains many typos: 1) use == instead of = in (boundary conditions); 2) use D[,r] instead of $\nabla _r$ 3) replace 'c[r,t] by (s[r, t]*e[r, t])/kappa; 4) to avoid division by 0 exclude e[r,0]== 0; 5) don't use Toolbox6) define constants kappa, $D_r$ ;7) add boundary conditions. – Alex Trounev May 2 at 12:24
• Please include the error message name. – Michael E2 May 2 at 12:27
• The first error @AlexTrounev points out sounds like the cause of the NDSolve error. Related: mathematica.stackexchange.com/questions/40314/… – Michael E2 May 2 at 12:29
• @MichaelE2 Second::shdw: Symbol Second appears in multiple contexts {AutomaticUnits,Prototypes}; definitions in context AutomaticUnits may shadow or be shadowed by other definitions. Fifth::shdw: Symbol Fifth appears in multiple contexts {AutomaticUnits,Prototypes}; definitions in context AutomaticUnits may shadow or be shadowed by other definitions. Molecule::shdw: Symbol Molecule appears in multiple contexts {AutomaticUnits,System}; definitions in context AutomaticUnits may shadow or be shadowed by other definitions. – Alex Trounev May 2 at 15:49