How to Solve equation using Eulers method in Matlab?

Question is as follows:-

Solve the following initial value problem over the interval from t = 0 to 1 where y(0) = 1.

dy/dt = yt^2 - 1.1y

• (a) analytically (showing the intermediate steps in the comments),

• (b) using the explicit Euler’s method with h = 0:5,

• (c) using the explicit Euler’s method with h = 0:25

Note: The Symbolic Math Toolbox should NOT be used.

Below is my code . I wanted to know my mistake if any.

%for h=0.5
h=0.5;
t=0:h:1;
y=zeros(size(t));
y(1)=1;
n=numel(y);

for i = 1:n-1
    dydt= (y(i)*t(i).^2)-(1.1*y(i))
    y(i+1) = y(i)+(dydt*h) 
    disp(y(i));
end

dydt = -1.1000

y = 1×3

1.0000 0.4500 0

     1

dydt = -0.3825

y = 1×3

1.0000 0.4500 0.2587

    0.4500

%for h=0.25
h1=0.25;
t1=0:h1:1;
y1=zeros(size(t1));
y1(1)=1;
n1=numel(y1)

n1 = 5

for i = 1:n1-1
    dydt1= (y1(i)*t1(i).^2)-(1.1*y1(i))
    y1(i+1)=y1(i)+(dydt1*h1) 
    disp(y1(i));
end

dydt1 = -1.1000

y1 = 1×5

1.0000 0.7250 0 0 0

     1

dydt1 = -0.7522

y1 = 1×5

1.0000 0.7250 0.5370 0 0

    0.7250

dydt1 = -0.4564

y1 = 1×5

1.0000 0.7250 0.5370 0.4229 0

    0.5370

dydt1 = -0.2273

y1 = 1×5

1.0000 0.7250 0.5370 0.4229 0.3660

    0.4229

Display in a plot

• the analytical result (a) as a black solid line, and

• the numerical results (b - c) as solid lines with point markers in different color

• with the corresponding labels of the axes and legend.

% analytical sol(plz check for this too)
T=[0 1]

T = 1×2

0 1

Y=[1 -0.766]   

Y = 1×2

1.0000 -0.7660

% Graph
plot(t,y,'r',"DisplayName","h=0.5");
hold on 
plot(t1,y1,'b',"DisplayName","h=0.25");
plot(T,Y,'k',"DisplayName","Anlaytical sol");
legend
grid on;

Answer 1

[Alan Stevens]

Here's part (a) for you - definitely not a straight line!

[Samson David Puthenpeedika]

Thankyou! is the rest part correct?

[Alan Stevens]

Yes