how to Plot improved Euler's Method

I am trying to plot Improved Euler's method but I only get an empty graph. I have no idea what is wrong. Here is my code.

fprintf('Imp Euler With h=0.1')
dy=@(x,y) (x+y-1)^2;
f=@(x,y)(tan(x+(pi/4))-x+1);
x0=0;
h=0.1;
xn=0.5;
y=2;
fprintf('x               y(Imp. Euler)   y(Actual) \n')
fprintf('%f\t %f\t %f\t \n',x0,y,f(x0));
for x=x0:h:xn-h
    i1=dy(x,y);
    i2=dy(x+h,y+(h*i1));
    y = y + (h*((i1+i2)/2));
    x=x+h;
    fprintf('%f\t %f\t %f\t \n',x,y,f(x));
end
plot(x,y,'r','linewidth',2);
hold on
legend ('Improved Euler')

[William]

Hello,

The problem is that you need an array of points to plot a graph. I your code, x is an array but y is a scalar. Try this:

fprintf('Imp Euler With h=0.1')
dy=@(x,y) (x+y-1)^2;
f=@(x,y)(tan(x+(pi/4))-x+1);
x0=0;
h=0.1;
xn=0.5;
fprintf('x               y(Imp. Euler)   y(Actual) \n')
fprintf('%f\t %f\t %f\t \n',x0,y,f(x0));
x = x0:h:xn;
n = length(x);
y = zeros(1,n);
y(1) = 2;
for j = 1:n-1
    i1=dy(x(j),y(j));
    i2=dy(x(j+1),y(j)+(h*i1));
    y(j+1) = y(j) + (h*((i1+i2)/2));
    fprintf('%f\t %f\t %f\t \n',x(j),y(j),f(x));
end
plot(x,y,'r','linewidth',2);
hold on
legend ('Improved Euler');

Answer 1

[Reshma Nerella]

Hi,

When you try to plot a line with scalar inputs, the plot doesn't show up in the figure unless you use a Marker like *, +, . etc

In this line of code

plot(x,y,'r','linewidth',2);

x, y are scalars. Since you didn't specify any Marker, you got an empty figure.

Instead try

plot(x,y,'r*','linewidth',2);

Hope this helps!

[Dina Abd Elkader]

Unfortunately the problem is still the same. The code generates correct approximation values, and an empty graph. Also I have no idea how to plot the absolute error (AR).