How can I make plot lines different colors when solving PDE?

I am attempring to plot solutions of a system of PDE's, my code gives me the solutions I am looking for but I require lines from u and v to be corresponding colors. I have attempted this in the following for loop but I keep getting an error saying

Error using plot

Vectors must be the same length.

Error in untitled5 (line 12)

plot(x, u(:,1),'--',line_color(k))

How can I ensure that each line of my plot is a different color and are corresponding?

m = 0;
x = -100:0.1:100;
t=0:5:40;

sol=pdepe(m,@eq2,@eq2IC,@eq2BC,x,t);

u=sol(:,:,1);
v=sol(:,:,2);
line_color = ['r' 'g' 'b' 'c' 'm' 'y' 'k' '#7E2F8E' '#A2142F' ];

for k = 1:length(line_color)
    plot(x, u(:,1),'--',line_color(k))
end
hold on
for k = 1:length(line_color)
    plot(x, v(:,1),'-', line_color(k))
end
grid("on")
title('Density of population at x for given t')
ylabel('Density of population (u(x,t)/v(x,t)' )
xlabel('Location (x)')
legend('u(x,0)', 'u(x,5)', 'u(x,10)','u(x,15)', 'u(x,20)', 'u(x,25)', 'u(x,30)', 'u(x,35)', 'u(x,40)','v(x,0)', 'v(x,5)', 'v(x,10)','v(x,15)', 'v(x,20)', 'v(x,25)', 'v(x,30)', 'v(x,35)', 'v(x,40)')
lcn('bestoutside')
hold off

function [c,f,s] = eq2(x,t,u,dudx)
D = 2;
r = 1.5;
a = 0.6;
b = 0.7;

c=[1; 1];
f = [dudx(1);
    D*dudx(2)];
s=[u(1)*(1-u(1)-a*u(2));
    r*u(2)*(1-u(2)-b*u(1))];
end


function u0 = eq2IC(x)
  if (x>=-1 && x<=1)
    u0 = [1;0.2];
  else 
    u0 = [1;0];
  end
end

function [pl,ql,pr,qr] = eq2BC(xl,ul,xr,ur,t) % Boundary Conditions
pl = [0;0];
ql = [1;1];
pr = [0;0];
qr = [1;1];
end

Answer 1

[Star Strider]

There are problems referenceing ‘u’ and ‘v’ since they are both (9x2001) matrices, so to be comkpatible with ‘x’ address the rows, not the columns. Create ‘line_color’ as a cell array (and then use cell array indexing to refer to its elements), since the square brackets [] are a concatenation operator in MATLAB, making the last two elements indecipherable otherwise. There are still a few problems, however this addresses the requested problems.

m = 0;
x = -100:0.1:100;
t=0:5:40;

sol=pdepe(m,@eq2,@eq2IC,@eq2BC,x,t);

u=sol(:,:,1);
v=sol(:,:,2);
line_color = {'r' 'g' 'b' 'c' 'm' 'y' 'k' '#7E2F8E' '#A2142F' };

for k = 1:length(line_color)
    plot(x, u(1,:),'--','Color',line_color{k})
end
hold on
for k = 1:length(line_color)
    plot(x, v(1,:),'-', 'Color',line_color{k})
end
grid("on")
title('Density of population at x for given t')
ylabel('Density of population (u(x,t)/v(x,t)' )
xlabel('Location (x)')
hl = legend('u(x,0)', 'u(x,5)', 'u(x,10)','u(x,15)', 'u(x,20)', 'u(x,25)', 'u(x,30)', 'u(x,35)', 'u(x,40)','v(x,0)', 'v(x,5)', 'v(x,10)','v(x,15)', 'v(x,20)', 'v(x,25)', 'v(x,30)', 'v(x,35)', 'v(x,40)');

Warning: Ignoring extra legend entries.

hl.Location = 'bestoutside';
hold off

function [c,f,s] = eq2(x,t,u,dudx)
D = 2;
r = 1.5;
a = 0.6;
b = 0.7;

c=[1; 1];
f = [dudx(1);
    D*dudx(2)];
s=[u(1)*(1-u(1)-a*u(2));
    r*u(2)*(1-u(2)-b*u(1))];
end


function u0 = eq2IC(x)
  if (x>=-1 && x<=1)
    u0 = [1;0.2];
  else 
    u0 = [1;0];
  end
end

function [pl,ql,pr,qr] = eq2BC(xl,ul,xr,ur,t) % Boundary Conditions
pl = [0;0];
ql = [1;1];
pr = [0;0];
qr = [1;1];
end

.