solving a system of pdes using pdepe

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Ricardo Machado 2020-12-22

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https://ww2.mathworks.cn/matlabcentral/answers/700105-solving-a-system-of-pdes-using-pdepe

评论： Bill Greene 2020-12-23

在 MATLAB Online 中打开

So i have the follwing system of pdes:

where

The symmetry boundary conditions are:

The other two boundary conditions are given by:

and

Parameter values are: k1 = 5 ,k2 =6 , C=8.

So this is the function code:

function [c,f,s] = pdefun(x,t,u,dudx) 
% Equation to solve
c = [1; 1];
if x <= 2
    f = 5*dudx;
else
    f = 6*dudx;
end
%k1 and k2.
end
% ---------------------------------------------
function u0 = pdeic(x) % Initial Conditions
u0 = [10; 0];
end
% ---------------------------------------------
function [pl,ql,pr,qr] = pdebc(xl,ul,xr,ur,t) % Boundary Conditions
pl = [0; 0];
ql = [0; 0];
pr = [e; f]; 
qr = [g; h];
end
% ---------------------------------------------

Then to solve the equation:

x = [0 0.1 0.2 0.3 0.4 0.45 0.475 0.5 0.525 0.55 0.6 0.7 0.8 0.9 0.95 0.975 0.99 1];
t = [0 0.001 0.005 0.01 0.05 0.1 0.5 1];
m = 2;
sol = pdepe(m,@pdefun,@pdeic,@pdebc,x,t);
u1 = sol(:,:,1);
u2 = sol(:,:,2);

To plot the solution:

surf(x,t,u1) %or u_{2}
title('u_1(x,t)')
xlabel('Distance x')
ylabel('Time t')

Just asking how do you write down the boundary conditions to make it suitable for pdepe as the examples provided on the matlab website don't help much with putting the boundary conditions in the standard form?