plot line after using fprintf

I tried to solve some equation with using Euler's formula (code is presented below) and everything is all right with one small problem. As shown below, finally I would like to plot 2 functions: 'f(x)' which is analitical solution and 'y(x)' which corresponds to Euler's solutions.

I want 'f(x)' to be plotted as continuous line (not only points). But the plot is rebelling and shows only points :(

Anybody could explains this?

dy = @(x,y)y-x^2+1;                  % differential equation
f = @(x)((x+1)^2)-0.5*exp(x);        % analytical solution

x0 = 0;     % initial point of interval
xf = 2;     % final point of interval
y = 0.5;    % initial condition of value of y at x0
h = 0.1;    % step size for side edge

fprintf('x(i)\t\t y_Euler(i)\t\t y_analitical(i)\n')            % data table header
fprintf('%f\t %f\t\t %f\n',x0,y,f(x0));

for x = x0 : h : xf-h
    y = y + dy(x,y)*h;  % Euler formula
    x = x + h;          % here we compute x as the next step
    
    fprintf('%f\t %f\t\t %f\n',x,y,f(x));           % print results
    
    figure(1)
    plot(x,f(x),'rx-','LineWidth',2)
    hold on
    plot(x,y,'bo')
    title('Euler`s method and exact solution')
    xlabel('x','FontSize',12,'FontWeight','bold','Color','black')
    ylabel('y','FontSize',12,'FontWeight','bold','Color','black')
    legend('Analytical solution','Euler method')
    grid on; grid minor
end

Answer 1

[Asad Mirza]

The issue is x, f(x), and y are all discrete points every loop. They have no vectorized connection to their previous point. One solution I can see is only plot the result afterwards and have the x, f(x), and y be vectorized.

dy = @(x,y)y-x^2+1;                  % differential equation
f = @(x)((x+1)^2)-0.5*exp(x);        % analytical solution
x0 = 0;     % initial point of interval
xf = 2;     % final point of interval
y = 0.5;    % initial condition of value of y at x0
h = 0.1;    % step size for side edge
fprintf('x(i)\t\t y_Euler(i)\t\t y_analitical(i)\n')            % data table header
fprintf('%f\t %f\t\t %f\n',x0,y,f(x0));
count=1;
for x = x0 : h : xf-h
    y = y + dy(x,y)*h;  % Euler formula
    x = x + h;          % here we compute x as the next step
    
    fprintf('%f\t %f\t\t %f\n',x,y,f(x));           % print results
 
    xplot(count)=x;
    yplot(count)=y;
    funplot(count)=f(x);
    count=count+1;
end

figure(1)
plot(xplot,funplot,'rx-','LineWidth',2)
hold on
plot(xplot,yplot,'bo')
title('Euler`s method and exact solution')
xlabel('x','FontSize',12,'FontWeight','bold','Color','black')
ylabel('y','FontSize',12,'FontWeight','bold','Color','black')
legend('Analytical solution','Euler method')
grid on; grid minor

[Elzbieta Trynkiewicz]

Thank you a lot! Now it works great! :)

Answer 2

[Walter Roberson]

At any one time, x is scalar, and f(x) is scalar. So at any one time, you are asking to plot() a pair of scalars. When you ask to plot scalars, MATLAB creates a point there that is not joined to anything.

In order to get what you want, you need to record the x and f(x) values somewhere, and move the plotting to after the loop when you have the values available.

Hint:

xvals = x0 : h : xf-h;
numx = length(xvals);
fx = zeros(1, numx);

for xidx = 1 : numx
    x = xvals(xidx);
    fx(xidx) = f(x);
end

[Elzbieta Trynkiewicz]

Agrees, thanks for paying attention! But still it does not work.