Hello,
I have a system of coupled 1 PDE and 2 ODE and I’m using PDEPE solver. The model is coded according to the standard as in other systems of coupled equations however, it is not yet working properly and I don’t understand why.
The system is:
dCb/dt = Deff*(1/r)*d/dr(r*dCb/dr)-Rb
where:
Rb = kf*Cb*Cg – kr*Cbg
dCg/dt = n*kr*Cbg – n*kf*Cb*Cg
dCbg/dt = -kr*Cbg + kf*Cb*Cg
Boundary Conditions:
For r = 0 -Deff*dCb/dr = PCp = P*(Cp0*[alpha*exp(-lambda1*t)+(1-alpha)*exp(-lambda2*t)])
For r = 75 µm
-Deff*dCb/dr = 0
Initial Conditions:
Cb = 0; Cg = 1000; Cbg = 0
The code I made is as follows:
n = 2; %IgG Antibody alpha = 0.27; kr = 5.3E-5; %s^-1 kf = 2.7E-5; %(nM.s)^-1 lambda1 = 1.9E-4; %s^-1 lambda2 = 7.4E-6; %s^-1 Cp0 = 100; %nM Deff = 1.3; %µm^2/s P = 0.0057; %µm/s R = 75; %µm Ri = 10; %µm
m = 1; x = linspace(0,R,5); %Spacial Coordinates t = linspace(0,28800,7200); %Time Coordinates ==== 80 h!!!
C = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);
u1 = C(:,:,1); u2 = C(:,:,2); u3 = C(:,:,3);
function [c,f,s]=pdex1pde(~,~,u,DuDx)
c = [1; 1; 1];
f = [Deff; 0; 0].*DuDx;
s = [-kf*u(1)*u(2)+kr*u(3); n*kr*u(3)+kf*u(2)*u(1); -kr*u(3)+kf*u(1)*u(2)];
end
% ------------------------------------------------------
function u0 = pdex1ic(~)
u0 = [0; 1000; 0];
end
% ------------------------------------------------------
function [pl,ql,pr,qr] = pdex1bc(~,ul,~,ur,t)
pl = [P*Cp0*(alpha*exp(-lambda1*t)+(1-alpha)*exp(-lambda2*t)); 0; 0];
ql = [Deff; 0; 0];
pr = [0; ur(2); ur(3)];
qr = [-Deff; 0; 0];
end
