Going from Euler's method to trapezoidal rule

Question

Chloe Keller 2018-7-15

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/410465-going-from-euler-s-method-to-trapezoidal-rule

回答： Swaraj 2023-2-9

I used Euler's Method to solve y'= 1−t+4y with y(0) = 1 on the interval [0, 2], h = 0.01. I posted my code below. How would I edit this code to solve the same problem using the Trapezoidal Rule?

if true
syms t y
f=@(t,y) 1-t+4.*y;
t=0;
y=1;
h=.01;
n=(2-0)/h;
for i=1:n
  m=f(t(i),(y(i)));
  y=[y, y(i)+m*h]; %y(i+1)=y(i)+m*h
  t=[t, t(i)+h]; %t(i+1)=t(i)+h
end
for i=1:length(t)
  fprintf('%5.4f  |  %5.4f\n',t(i),y(i))
end
end

2 个评论
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DINU ANDREEA-EMILIA 2020-6-3

Did you find the answer to your question? Cause i have to do the exact same thing

James Tursa 2020-6-3

You could look here:

https://en.wikipedia.org/wiki/Trapezoidal_rule_(differential_equations)

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Answer 1

Swaraj 2023-2-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/410465-going-from-euler-s-method-to-trapezoidal-rule#answer_1167360

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You would have to modify the calculation of the intermediate value m as follows:

if true
syms t y
f=@(t,y) 1-t+4.*y;
t=0;
y=1;
h=.01;
n=(2-0)/h;
%Changed Part Start
for i=1:n
  m1 = f(t(i),y(i));
  m2 = f(t(i) + h/2, y(i) + m1*h/2);
  y = [y, y(i) + m2*h];
  t = [t, t(i) + h];
end
%Changed Part End
for i=1:length(t)
  fprintf('%5.4f  |  %5.4f\n',t(i),y(i))
end
end