How to plot a 2D graph from a surface?

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Aldo Leal Garcia
Aldo Leal Garcia 2016-8-4
I have the next code wich is an explicit finite difference scheme. I need to plot a (x,y) with respect from the time, what I need is a graphic for the evolution of "u" and "v" with respect from time.
Here is the code:
% Modelo de Sel'kov 2D utilizando un esquema FTCS de diferencias finitas
function []=RDzeroux(~,~,~)
clear all
close all
% Llenado del mallado
N = 100;
h = 1/N; % Tamaño de paso de x y y
x = h.*(0:N); % Coordenadas del mallado en x
y = h.*(0:N); % Coordenadas del mallado en y
[xx,~] = meshgrid(x,y); % Coordenadas x e y en 2D
dt = 10.*h;%0.8.*h.^2; % tamaño de paso temporal (usualmente pequeño)
% Valores de los parámetros
a = 0; %0; %0.08;
b = 0.9502; %0.6; %0.9502;
Du = 0.0002;
Dv = 0.0001;
% Initial data at t=0:
% us = (a+b); % u steady state
% vs = b/us^2; % v steady state
% u = (a+b)*ones(size(xx)); % u steady state
% v = (b./u.^2); % v steady state
u = b.*ones(size(xx)) + 0.01.*randn(size(xx)); % Pequeñas perturbaciones cercas del estado estable
v = b./(a+b).^2.*ones(size(xx)) + 0.01.*randn(size(xx));
t = 0;
tmax = 1;
fig = figure('position',[100 100 850 600]);
nsteps = round(tmax/dt); % número de pasos
vidObj = VideoWriter('Selkov2Datro.avi');
vidObj.Quality = 100;
vidObj.FrameRate = 10;
open(vidObj);
for n = 1:nsteps
t = t+dt;
uE = u(:,[2:N+1 N]);
uW = u(:,[2 1:N]);
uN = u([2 1:N],:);
uS = u([2:N+1 N],:);
vE = v(:,[2:N+1 N]);
vW = v(:,[2 1:N]);
vN = v([2 1:N],:);
vS = v([2:N+1 N],:);
% Squema FTSC
u2v = u.^2.*v;
u = u + dt*(a.*v - u + u2v) + Du*dt*(uE+uW+uN+uS-4*u)/h^2;
v = v + dt*(b - a.*v- u2v) + Dv*dt*(vE+vW+vN+vS-4*v)/h^2;
subplot(1,2,1)
p = pcolor(x, y, u);
title(['t=', num2str( t ), ' ATP(u)']);
colorbar;
set(p, 'EdgeColor', 'none', 'FaceColor', 'interp');
subplot(1,2,2)
p = pcolor(x, y, v);
title(['t=', num2str( t ), ' ADP(v)']);
colorbar;
set(p, 'EdgeColor', 'none', 'FaceColor', 'interp');
% plot(x,u,'g.-', 'linewidth',1);
% hold on;
% plot(x,v,'r.-', 'linewidth',1);
% hold off;
% legend('ATP','ADP')
% axis([0 1 0 2])
% title(['t = ', num2str(t)],'fontsize',24)
% drawnow;
% tmax
% t
writeVideo(vidObj, getframe(fig));%gca));
end
close(gcf)
close(vidObj);
winopen('Selkov2Datro.avi')
% Graficas solución
figure(1);
s = surf(x,y,u);
set(s, 'EdgeColor', 'none', 'FaceColor', 'interp');
title(['u en t = ' num2str(t)],'fontsize',16)
xlabel('<----x---->')
ylabel('<----y---->')
zlabel('<----t---->')
figure(2)
s = surf(x,y,v);
set(s, 'EdgeColor', 'none', 'FaceColor', 'interp');
title(['v en t = ' num2str(t)],'fontsize',16)
xlabel('<----x---->')
ylabel('<----y---->')
zlabel('<----t---->')
figure(3);
p = pcolor(x, y, u);
colorbar;
set(p, 'EdgeColor', 'none', 'FaceColor', 'interp');
figure(4);
q = pcolor(x, y, v);
colorbar;
set(q, 'EdgeColor', 'none', 'FaceColor', 'interp');
Please, help me to do that, what I need is something like this:
where the red line is "u" and the green line is "v".
Please help me add something in my code.

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