Can't get plot to work

Hello Mathworks team!

I created this Euler's method code below but can't get the graph to show anything at all. Even if I make a separate code with just xn=1 yn=1, plot(xn,yn), the graph shows up but nothing on it. Any help would be much appreciated.

%Euler's Method
h=.25;%step size
xinitialcondition=0;%initial condition for x
yinitialcondition=1;%initial condition for y
n=0;%start at 0
xn=xinitialcondition;
yn=yinitialcondition;
f=@(xn,yn) (2*(cos(xn))*yn);%the function to be evaluated
while xn < 10%what value do you want it estimated to
    xn = (xinitialcondition) + ((n) .* (h));
    [n xn yn]
        yn = (yn) + ((h) .* f(xn,yn));
        if xn >= 10
            break
        end
        plot(xn,yn,"r-")
        hold on
    n=n+1;
end
hold off

Answer 1

[Walter Roberson]

%Euler's Method
h=.25;%step size
xinitialcondition=0;%initial condition for x
yinitialcondition=1;%initial condition for y
n=0;%start at 0
xn=xinitialcondition;
yn=yinitialcondition;
f=@(xn,yn) (2*(cos(xn))*yn);%the function to be evaluated
while xn < 10%what value do you want it estimated to
    xn = (xinitialcondition) + ((n) .* (h));
    [n xn yn]
        yn = (yn) + ((h) .* f(xn,yn));
        if xn >= 10
            break
        end
        plot(xn,yn,"r-*")  %CHANGED
        hold on
    n=n+1;
end

ans = 1×3

0 0 1

ans = 1×3

1.0000 0.2500 1.5000

ans = 1×3

2.0000 0.5000 2.2267

ans = 1×3

3.0000 0.7500 3.2037

ans = 1×3

4.0000 1.0000 4.3758

ans = 1×3

5.0000 1.2500 5.5579

ans = 1×3

6.0000 1.5000 6.4342

ans = 1×3

7.0000 1.7500 6.6618

ans = 1×3

8.0000 2.0000 6.0681

ans = 1×3

9.0000 2.2500 4.8055

ans = 1×3

10.0000 2.5000 3.2961

ans = 1×3

11.0000 2.7500 1.9758

ans = 1×3

12.0000 3.0000 1.0627

ans = 1×3

13.0000 3.2500 0.5367

ans = 1×3

14.0000 3.5000 0.2699

ans = 1×3

15.0000 3.7500 0.1435

ans = 1×3

16.0000 4.0000 0.0846

ans = 1×3

17.0000 4.2500 0.0570

ans = 1×3

18.0000 4.5000 0.0443

ans = 1×3

19.0000 4.7500 0.0396

ans = 1×3

20.0000 5.0000 0.0403

ans = 1×3

21.0000 5.2500 0.0461

ans = 1×3

22.0000 5.5000 0.0579

ans = 1×3

23.0000 5.7500 0.0784

ans = 1×3

24.0000 6.0000 0.1121

ans = 1×3

25.0000 6.2500 0.1659

ans = 1×3

26.0000 6.5000 0.2489

ans = 1×3

27.0000 6.7500 0.3704

ans = 1×3

28.0000 7.0000 0.5358

ans = 1×3

29.0000 7.2500 0.7377

ans = 1×3

30.0000 7.5000 0.9472

ans = 1×3

31.0000 7.7500 1.1114

ans = 1×3

32.0000 8.0000 1.1691

ans = 1×3

33.0000 8.2500 1.0840

ans = 1×3

34.0000 8.5000 0.8749

ans = 1×3

35.0000 8.7500 0.6116

ans = 1×3

36.0000 9.0000 0.3728

ans = 1×3

37.0000 9.2500 0.2030

ans = 1×3

38.0000 9.5000 0.1030

ans = 1×3

39.0000 9.7500 0.0517

ans = 1×3

40.0000 10.0000 0.0272

hold off

[Walter Roberson]

plot() only draws a line if there are two adjacent finite values in the same call. You are only plotting one point at a time, so it cannot draw lines.

[Matt Baron]

Thank you!

Answer 2

[KSSV]

Save into a Matrix and plot all at once:

%Euler's Method
h=.25;%step size
xinitialcondition=0;%initial condition for x
yinitialcondition=1;%initial condition for y
n=0;%start at 0
xn=xinitialcondition;
yn=yinitialcondition;
f=@(xn,yn) (2*(cos(xn))*yn);%the function to be evaluated
A = zeros([],2) ; 
while xn < 10%what value do you want it estimated to
    xn = (xinitialcondition) + ((n) .* (h));   
        yn = (yn) + ((h) .* f(xn,yn));
        if xn >= 10
            break
        end               
        n=n+1;
        A(n,:) = [xn yn]   ; 
end
plot(A(:,1),A(:,2))

[Matt Baron]

Perfect, I will examine this and learn.

[Matt Baron]

Hmm.. I guess I can't accept 2 answers....

[KSSV]

You can vote....

[Matt Baron]

Like whose is better? lol

[Matt Baron]

Do I have the questions correct in bold below;

A = zeros([],2) ; %so this is like creating an empty matrix that will be x by 2 for future use?

while xn < 10%what value do you want it estimated to

xn = (xinitialcondition) + ((n) .* (h));

yn = (yn) + ((h) .* f(xn,yn));

if xn >= 10

break

end

n=n+1;

A(n,:) = [xn yn] ; %this is inputting xn yn into the nth row of matrix A?

end

plot(A(:,1),A(:,2)) %this plots matrix A all rows of column 2 vs matrix A all rows of column 1?

[Matt Baron]

It wasn't working with n=1 so I re-wrote the code using matrices according to your code above and it worked!!

This looks so much better.

h=.05;%step size

init=[1 1];%initial conditions for x and y

n=1;%start at 1

x=init(1,1);

y=init(1,2);

A=zeros([],2);%create an empty 0 by 2 matrix for later

f=@(x,y) (.2 * x * y);%the function to be evaluated

while x <= 1.5%what value do you want it estimated to

A(n,:)=[x y];%input x and y into row n

y = (y + ((h) * f(x,y)));

x = (init(1,1) + ((n) * (h)));

if x > 1.5

break

end

n=n+1;

end

plot (A(:,1),A(:,2))%plot y vs x