How to imply conditional boundary condition in PDEPE?

Hi all,

I have problem my left side boundary condition is time dependent and it is

when I try to apply pdepe in matlab I couldn't write my pl values according the time values.

P.S. I'm a new learner please be kind when you are replying. Thanks :)

clear all;

clc;

close all;

L = 1000;

x = linspace(0,L,1001);

t = [linspace(0,5,20), linspace(5.1,50,10)];

m = 0;

sol = pdepe(m,@heatpde,@heatic,@heatbc,x,t);

colormap hot

imagesc(x,t,sol)

colorbar

xlabel('Distance x','interpreter','latex')

ylabel('Time t','interpreter','latex')

title('Heat Equation for $0 \le x \le 1000$ and $0 \le t \le 50$','interpreter','latex')

function [c,f,s] = heatpde(x,t,u,dudx)

c = 0.02;

f = dudx;

s = 0;

end

function u0 = heatic(x)

u0 = 50-(0.01*x);

end

function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)

g=50-0.1*(t-1);

if (t >= 0) && (t <= 20)

pl = ul-50;

ql = 0;

elseif (t > 20) && (t <= 50)

pl = ul - g;

ql = 0;

end

pr = ur-40;

qr = 0;

end

[Sait Mutlu Karahan]

I need help urgently guys!

[Torsten]

Your heatbc function looks fine to me.

What's the problem (apart from the discontinuity at t = 20 in your boundary condition at x=0 that pdepe most probably will not manage) ?

[Sait Mutlu Karahan]

heatbc does not take into account the condition it only takes that 50 as the right side boundary condition

[Torsten]

heatbc does not take into account the condition it only takes that 50 as the right side boundary condition

You mean left side boundary condition ?

Then either tighten RelTol and AbsTol for the ode integrator or - even better - integrate up to t = 20 and restart the solver with the solution at t = 20 as initial condition and with a function heatbc_for_t_greater_20 in which you define the boundary condition for ul for t>20.

[Sait Mutlu Karahan]

Thanks Torsten, I seperated and applied that. However now I have another problem because I got two different colormap. How can I merge them to show in a single graph?

[Torsten]

Concatenate the two solutions "sol1" and "sol2" in one solution array "sol" and plot as usual.

I think this is what you meant by "different colormap" ? Because you plotted the two solution matrices separately ?

[Sait Mutlu Karahan]

yes I'm talking about that but I couldn't find how to do that

[Torsten]

t = [t1;t2];
sol = [sol1(:,:,1);sol2(:,:,1)];