how to make matlab calculate (x) in PDE

i have one PDE with three variable x,t,u.

so i defind the initial and final value of u, and give range of t, but no matter how much my t range is, it's still met the final u value

how to make matlab calculate x variable with the given range to t in the boundry condition of u

as example if my t is from 10-20, i want matlab to plot the x result at this time

this my command:

function [c,f,s]=eqn11(x,t,u,DuDx,T)
c=1;
f=(1.34*10^-6)*exp(-16000/(8.314.*T))*DuDx;
s=0;
end
------------------------------------------------------------------------------

function [pl,ql,pr,qr]=bc11(xl,ul,xr,ur,t,kp,kd)
pl=xl;
ql=-(kp*5.3347*(5*exp(-kd*t))/0.002);
pr=xr;
qr=-111.8507355;
end
------------------------------------------------------------------------------

function value=initial11(u)
value=5.3347;
-----------------------------------------------------------------------------

kp0=140270;
Eap=43900;
kd0=0.355;
Ead=17400;
T=[333 334 335 336 337 338 339 340];
m=2;
t=linspace(0,120,100)
u=linspace(5.3347*5/0.002,111.8507355,100)
hold on
for i = 1:numel(T)
    kp=kp0*exp(-Eap/(8.314*T(i)));
    kd=kd0*exp(-Ead/(8.314*T(i)));
    x=pdepe(m,@(x,t,u,DuDx)eqn11(x,t,u,DuDx,T(i)),@initial11,@(xl,ul,xr,ur,t)bc11(xl,ul,xr,ur,t,kp,kd),u,t);
end
hold off
plot(x(2,:),u);
xlabel('radius');
ylabel('concentration');

i_hope_my_problem_is_clear

Answer 1

[Hassaan]

% Define constants and parameters
kp0 = 140270;
Eap = 43900;
kd0 = 0.355;
Ead = 17400;
T = [333 334 335 336 337 338 339 340]; % Temperature range
m = 2; % Symmetry parameter for pdepe
t = linspace(0, 120, 100); % Time range
x = linspace(0, 1, 100); % Spatial domain
u0 = 5.3347; % Initial concentration

% Loop over temperatures
for i = 1:length(T)
    kp = kp0 * exp(-Eap / (8.314 * T(i)));
    kd = kd0 * exp(-Ead / (8.314 * T(i)));

    % Define the PDE function inline
    eqn11 = @(x, t, u, DuDx) deal(1, (1.34 * 10^-6) * exp(-16000 / (8.314 * T(i))) * DuDx, 0);

    % Define the initial condition function inline
    initial11 = @(x) u0;

    % Define the boundary condition function inline
    bc11 = @(xl, ul, xr, ur, t) deal(0, 1, 0, 1); % Modify as per your BCs

    % Solve the PDE
    sol = pdepe(m, eqn11, initial11, bc11, x, t);

    % Plotting results for a specific time range (e.g., t=10 to t=20)
    % Find indices of t that fall within the desired time range
    t_indices = find(t >= 10 & t <= 20);
    
    figure; % Open a new figure for each temperature
    hold on;
    for j = t_indices
        plot(x, sol(j, :)); % Plot x vs. concentration at this time
    end
    hold off;
    
    title(['Temperature = ', num2str(T(i)), ' K']);
    xlabel('Radius');
    ylabel('Concentration');
end

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[br]

thank you that really helpful, but let me ask one more thing, can i make matlab calculate x in the same PDE with the result of u at that time range

as if i chose t=0-60, then let matlab calculate u at this time, can i make this u as input again to the PDE to calculate x at this u

[Torsten]

For a fixed value of u and all times t, you want to calculate the x-values at which this fixed value of u is attained ?

[br]

yes

[br]

i want instead from give (x) value from 0 to 1, i want to calculate it at (u0) and (u final)