How to Solve equation using Eulers method in Matlab?

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Samson David Puthenpeedika
评论： Alan Stevens 2021-11-14
Ran in:
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;

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采纳的回答

Alan Stevens
Alan Stevens 2021-11-14
Here's part (a) for you - definitely not a straight line!

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