Euler's method code

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Mike Asmanis
Mike Asmanis 2021-6-18
评论： Mike Asmanis 2021-6-18
Hello , how can I code this : y'(t)=cos(t + y) y(0)=0 t[0,3] (exact solution y(t)=-t + 2arctan(t)) using Euler's method like the code below?
clc
clear all
close all
h=0.01;
N=100; % number of steps
y(1)=1;
for n=1:N
y(n+1)=y(n)+h*(-6*y(n));
x(n+1)=n*h;
end
plot(x,y)
hold on
x=0:0.01:1;
y=exp(-6*x); % exact solution
plot(x,y)

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回答（1 个）

Paul
Paul 2021-6-18
The code that is posted solves a differential equation of the form
y'(x) = f(x,y), y(0) = y0
and compares it to the exact solution
y(x) = some function of x
over the interval
x [0 1]
As it happens, your problem has the exact same form, with the independent variable being t instead of x and the endpoint of the interval is different.
  2 个评论
Mike Asmanis
Mike Asmanis 2021-6-18
I know that it solves a different equation , i just need to solve my problem using a simillar or the exact code like the one i posted.
Mike Asmanis
Mike Asmanis 2021-6-18
I'm getting Array indices must be positive integers or logical values.

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