Problem with PDE resolution

I get this error message when running my script PDEsol.m

>> PDEsol

Error using  / 
Matrix dimensions must agree.

Error in pdefun (line 13)
s = [dudx(2)-alpha*u(1)*u(2)*(1/(1-(u(1)/c)*(dudx(2))^(-1)));0];

Error in pdepe (line 246)
[c,f,s] = feval(pde,xi(1),t(1),U,Ux,varargin{:});

Error in PDEsol (line 10)
sol = pdepe(m,@pdefun,@pdeic,@pdebc,x,t)

This is myscript PDEsol.m :

%%
%select spatial and temporal mesh
%x = [0 0.005 0.01 0.05 0.1 0.2 0.5 0.7 0.9 0.95 0.99 0.995 1];
%t = [0 0.005 0.01 0.05 0.1 0.5 1 1.5 2];
x=[0:0.05:1];
t=[0:0.05:0.717];
%%
%solve PDEs system
m = 0;
sol = pdepe(m,@pdefun,@pdeic,@pdebc,x,t);
%%
%extract PDEs solutions
u1 = sol(:,:,1);
u2 = sol(:,:,1);
%%
%pressure oscillation's plot
surf(x,t,u2)
title('Pressure oscillations [Pa]')
xlabel('Distance x [m]')
ylabel('Time t [s]')

Below are the function call by PDEsol.m :

%PDEs system
function [c,f,s] = pdefun(x,t,u,dudx)
%
epsilon=1;
b=1;
c=200;
rho=1.22;
beta=b/(2*(c^3)*rho);
alpha=epsilon/(rho*(c^3));
%
c = [beta*((1/(1-(u(1)/c)*(dudx(2))^(-1)))+u(1)/(c*(1-(u(1)/c)*(dudx(2))^(-1))^2));1];
f = [0;0];       
s = [dudx(2)-alpha*u(1)*u(2)*(1/(1-(u(1)/c)*(dudx(2))^(-1)));0];
end 
%
%
%initial condition
function u0 = pdeic(x)
u0 = [sin(x);sin(x)];
end
%
%
%boundary condition
function [pl,ql,pr,qr] = pdebc(xl,ul,xr,ur,t)
pl = [ul(1); ul(2)];
ql = [0; 0];
pr = [ur(1)-0.9; ur(2)-0.9];
qr = [0; 0];
end

Answer 1

[Uday Pradhan]

Hi,

This error is produced because in the function “pdefun”, you have defined the variable “c” twice. In the first declaration “c” has a scalar value of 200. However,

c = [beta*((1/(1-(u(1)/c)*(dudx(2))^(-1)))+u(1)/(c*(1-(u(1)/c)*(dudx(2))^(-1))^2));1]; 

changes “c” into a 2 by 1 column vector. Hence, the later line

s = [dudx(2)-alpha*u(1)*u(2)*(1/(1-(u(1)/c)*(dudx(2))^(-1)));0]; 

causes a dimension mismatch error because “c” is no longer 200. To avoid this, choose a different name for the scalar value (200) or calculate the expression

Val = 1/(1-(u(1)/c)*(dudx(2))^(-1); 

before using it to calculate “s” in "pdefun".

[pierantonio lo greco]

Thank you so much !