Contents

% This script file computes for the transport equation u_t+cu_x=0 the
% followings: solution, characteristics

close all;
clear all;

speed=1;%input('Input the propagation speed ')

SECTION TITLE

Define the initial function

f_initial=@(x)exp(-2*(x-1).^2);

% Calculate and plot the solution in 3D
x=0:.1:8;
t=0:.1:5;
[X,Y]=meshgrid(x,t);

solution_u=@(x,t,c)f_initial(x-c*t);
Z=solution_u(X,Y,speed);

%mesh(X,Y,Z); %mesh plot
surf(X,Y,Z); %surface plot

xlabel('x','FontSize',14);
ylabel('t','FontSize',14);
zlabel('u','FontSize',14);
title('Solution u(x,t) of the transport equation with constant c')

%Instead of a 3D plot it makes a 2D plot of the colors used in surf
figure
pcolor(X,Y,Z);
title('2-D plot of the contours of the solution surface')
%figure
%contour(X,Y,Y,5)

% Calculate and plot a few characteristic curves (lines)
t=0:0.1:5;
x0=-9:.5:8;
m=size(x0,2);

char_curve=@(c,x0,t)x0+c*t;

figure
for i=1:m
    plot(char_curve(speed,x0(i),t),t)
    hold on
end;
hold off
axis([0 8 0 5]);
xlabel('x axis','FontSize',14);
ylabel('t axis','FontSize',14);
title('Characteristics')

Published with MATLAB® R2015b