I am finding issues in PDEPe which shows time integration failure again and again

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Aadityaamlan
Aadityaamlan 2024-6-21
回答： Umang Pandey 2024-7-16
"Warning: Failure at t=2.088125e-04. Unable to meet integration tolerances without reducing the step size
below the smallest value allowed (4.336809e-19) at time t. "
This message is being shown for running my code. I am uploading my code below.
clear all
clc
close all
m=0;
x=linspace(0,1,1001);
t=linspace(0,1,1001);
options = odeset('RelTol', 1e-3, 'AbsTol', 1e-6,'MaxStep', 0.1);
sol=pdepe(m,@coupledpde_BACD,@coupledic_BACD,@coupledbc_BACD,x,t,options);
b=sol(:,:,1);
figure(1)
surf(x,t,b)
xlabel('x')
ylabel('t')
zlabel('b(x,t)')
grid on
title('Bacterial distribution');
view([150 25])
colorbar
colormap jet
for j=[1 11 101]
ylim([0,1.2])
figure(2)
hold on
plot(x,b(j,:),LineWidth=2)
title("Particle Concentration Profile at t= (1, 11, 101)*td")
xlabel("Characteristic length")
ylabel('bacteria Concentration')
end
function [c,f,s]= coupledpde_BACD(x,t,u, dudx)
Db=10^-12;
Dc=10^-9;
X0=10^-9;
% X0=linspace(10^-11,10^-9,100);
% Db=linspace(10^-13,10^-12,100);
c=1;
s=0;
l=[pi/2 3*pi/2 5*pi/2];
A=4.*(cos(l)-1)./(2.*l-sin(2.*l));
mob_ratio=X0/Dc;
d_ratio=Db/Dc;
f=(d_ratio).*dudx-u*(mob_ratio)./(1+exp(-l(1)^2.*t).*A(1).*sin(l(1).*x)).*(exp(-l(1)^2.*t).*A(1).*cos(l(1).*x).*l(1));
end
function u0 = coupledic_BACD(x)
u0=1;
end
function [pl,ql,pr,qr]= coupledbc_BACD(xl,ul,xr,ur,t)
pl=ul;
ql=0;
pr=0;
qr=1;
end
please help me find the issue in the code
  4 个评论
显示 2更早的评论
Torsten
Torsten 2024-6-22
编辑：Torsten 2024-6-22
At the moment, you set
(d_ratio).*dudx(@x=1)-u(@x=1)*(mob_ratio)./(1+exp(-l(1)^2.*t).*A(1).*sin(l(1))).*(exp(-l(1)^2.*t).*A(1).*cos(l(1)).*l(1)) = 0
Is this what you mean by "zero neumann boundary condition" ?

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回答（1 个）

Umang Pandey
Umang Pandey 2024-7-16
Hi Aaditya,
This error message indicates that the problem you are trying to solve is too stiff for the ODE solver you are trying to use, or that it includes a singularity.
It has been explained by the MathWorks Support Staff in the following MATLAB answer:
https://www.mathworks.com/matlabcentral/answers/101581-why-do-i-receive-a-warning-about-integration-tolerance-when-using-the-ode-solver-functions#answer_110929
Hope this helps!
Best,
Umang

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