how to output quantities within pdefun, bcfun, icfun in pdepe

How to output quantities within pdefun, bcfun, icfun in pdepe? e.g. in pdefun:

function [c,f,s] = heatcyl(x,t,u,dudx)
c = 1;
f = dudx;
s = 0;
end

e.g. I want to output an extra quantity ex related to some intermediate value in pdefun, sth like [c,f,s,ex]=heatcyl(x,t,u,dudx), but which I'm sure isn't allowed.

Also want to output ic, but don't know the syntax, because feval(@ic,x) or pdeval(m,x,ic,x) doesn't work.

Answer 1

[Torsten]

After pdepe has finished, call "heatcyl" at the output times.

x = linspace(0,1,25);
t = linspace(0,1,25);
m = 1;
sol = pdepe(m,@heatcyl,@heatic,@heatbc,x,t);
ex = zeros(numel(t),numel(x));
for i = 1:numel(t)
  [~,dudx] = pdeval(m,x,sol(i,:,1),x);
  for j = 1:numel(x)
    [~,~,~,ex(i,j)] = heatcyl(x(j),t(i),sol(i,j,1),dudx(j));
  end
end
function [c,f,s,ex] = heatcyl(x,t,u,dudx)
c = 1;
f = dudx;
s = 0;
ex = c+1;
end
%----------------------------------------------
function u0 = heatic(x)
n = 2.404825557695773;
u0 = besselj(0,n*x);
end
%----------------------------------------------
function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)
n = 2.404825557695773;
pl = 0; %ignored by solver since m=1
ql = 0; %ignored by solver since m=1
pr = ur-besselj(0,n)*exp(-n^2*t);
qr = 0; 
end

Answer 2

[recent works]

In MATLAB's pdepe solver, the output arguments from pdefun, bcfun, and icfun are limited to the standard ones (c, f, s for pdefun, and pl, ql, pr, qr for bcfun). If you need to output additional quantities or evaluate the initial condition at specific points, you have to find alternative methods. To handle additional quantities within the pdefun, you can utilize global variables or nested functions to store and access these values. However, this approach is not very clean and can lead to potential issues with code readability and maintainability. Regarding evaluating the initial condition (ic), you can use pdeval after solving the PDE to evaluate the solution at any desired points. Here's how you can use pdeval to evaluate the initial condition at specific points:

% Define your PDE system

m = 0; % No of spatial variables

x = linspace(x_start, x_end, num_points);

t = linspace(t_start, t_end, num_time_points);

sol = pdepe(m,@pdefun,@icfun,@bcfun,x,t);

% Evaluate the solution at specific points

x_points_of_interest = [x1, x2, x3]; % Define the points where you want to evaluate the solution

t_points_of_interest = [t1, t2, t3]; % Define the time points where you want to evaluate the solution

u_at_points = pdeval(m, x, sol(end,:,:), x_points_of_interest);

u_at_time_points = pdeval(m, x, sol, t_points_of_interest);

• x_points_of_interest and t_points_of_interest are the spatial and temporal points where you want to evaluate the solution.
• sol(end,:,:) extracts the solution at the final time step.
• pdeval is then used to evaluate the solution at these points.

Remember to replace x_start, x_end, num_points, t_start, t_end, num_time_points, x1, x2, x3, t1, t2, and t3 with appropriate values relevant to your problem.

If you need to access quantities calculated during intermediate steps of the PDE solving process, you might need to modify the solver itself

[feynman feynman]

thank you! To extract x and t intrinsic solution data isn't hard, but what about extra quantities? e.g. does this work and if so, what's the syntax for extracting ex from heatcyl?

function [c,f,s,ex] = heatcyl(x,t,u,dudx)
c = 1;
f = dudx;
s = 0;
ex=c+1;
end