Mathematica: Help with NDSolve Error

[PenguInABox]

Mathematica: Help with NDSolve Error!

Hello All,

I am attempting to set up a model of an experiment I am running, but I keep getting the following error:
"NDSolve::ibcinc: Warning: Boundary and initial conditions are inconsistent."

However, I have checked all of my boundary conditions, and as far as I can tell they are compatible with the initial conditions. Can you see what I am missing?

Here is my script up to the offending line:


(*Clear Scope*)
ClearAll["Global`*"];
Clear[Derivative];
ClearGlobal[];
Remove["Global`*"];

(*Units:
length - mm
concentration - pmol/mm^3=uM
time - s
*)

(*Define Global Parameters*)
plotPoints=150;

(*Define Time Spans*)
inactiveRunTime=1000;(*time in time units to run model before activating Amplifier*)
activeRunTime=10;(*time in time units to run model after activating Amplifier*)

(*Define Gel Parameters*)
gelWidth=100;(*units:length*)
gelLength=100;(*units:length*)
gelDepth=1;(*units:length*)
sourceX=gelWidth/3;(*units:length*)
sourceY=gelLength/3;(*units:length*)
sourceZ=gelDepth/2;(*units:length*)
sourceWidth=10;(*units:length*)
sourceLength=5;(*units:length*)
sourceDepth=.9*gelDepth;(*units:length*)

(*Define Species Parameters*)
inputConcentration=1;(*units:concentration*)
dW25=150*10^-6;(*units:length^2/time*)
colorW25=(RGBColor[0,0,1]&);

(*Define Utility Functions*)
InputFunction[x_,y_,z_,cx_,cy_,cz_,w_,l_,d_]:=(1-1/(1+x^2))*(1-1/(1+(gelWidth-x)^2))*(1-1/(1+y^2))*(1-1/(1+(gelLength-y)^2))*(1-1/(1+z^2))*(1-1/(1+(gelDepth-z)^2))*Exp[-(x-cx)^2/(2*(w/2)^2)-(y-cy)^2/(2*(l/2)^2)-(z-cz)^2/(2*(d/2)^2)];

(*Construct Inputs*)
W25t0[x_,y_,z_]:=inputConcentration * InputFunction[x,y,z,sourceX,sourceX,sourceZ,sourceWidth,sourceLength,sourceDepth];

Plot3D[W25t0[x,y,sourceZ],{x,0,gelWidth},{y,0,gelLength},PlotRange -> All,PlotPoints -> plotPoints,Mesh->None]

diffuseInputs = NDSolve[{D[W25tA[t,x,y,z],t] == dW25*(D[W25tA[t,x,y,z],x,x]+D[W25tA[t,x,y,z],y,y]+D[W25tA[t,x,y,z],z,z]), W25tA[0,x,y,z]==W25t0[x,y,z],W25tA[t,0,y,z]==0,W25tA[t,gelWidth,y,z]==0,W25tA[t,x,0,z]==0,W25tA[t,x,gelLength,z]==0,Derivative[0,0,0,1][W25tA][t,x,y,0]==0,Derivative[0,0,0,1][W25tA][t,x,y,gelDepth]==0 },{W25tA},{t,0,inactiveRunTime},{x,0,gelWidth},{y,0,gelLength},{z,0,gelDepth}];

 

[Valkarie]

The error occurs on the last line, when I try to solve the differential equation using NDSolve. The main issue here is that your boundary and initial conditions are not compatible. The boundary conditions need to be consistent with the initial condition in order for the problem to be solvable. For example, if your initial condition specifies a particular value of the solution at time t=0, then your boundary conditions need to ensure that the solution does not deviate from this value. In addition, you may also need to adjust some of your parameters to get the desired behavior. For instance, if your diffusion coefficient is too low, then it may take too long for the system to reach equilibrium, resulting in an inconsistent solution. Finally, you may need to use additional methods to ensure that the solution is accurate. For instance, you could use MeshRefinement to refine the grid and increase the accuracy of the solution. I hope this helps!