How to Solve equation using Eulers method in Matlab?

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Samson David Puthenpeedika 2021-11-14

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https://ww2.mathworks.cn/matlabcentral/answers/1586049-how-to-solve-equation-using-eulers-method-in-matlab

评论： Alan Stevens 2021-11-14

采纳的回答： Alan Stevens

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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