I need a detailed explination of this code

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Sonja Cortes on 24 Mar 2020

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Answered: Ameer Hamza on 24 Mar 2020

So I have this script but i have no clue what it does, and I got the text that says that it is Euler's method to find an approximate solution to the startvalue problem

y' = sin(sqrt(x+y)) with the start value y(0) = 0.4

on the intervall [0,20]. And the following code implements Euler's methode and plots the graph for the approximat solution of y.

But I was wondering what this script does.

So can someone please explain to me line by line what it does?

ymark = @(x,y) sin(sqrt(x+y));
t = 0:0.01:20;
y = zeros(1,length(t));
y(1) = 0.04;
dt = diff(t);
for s= 1:length(t)-1
    y(s+1) = y(s)+dt(s)*ymark(t(s),y(s));
end
plot(t,y)

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John D'Errico on 24 Mar 2020

Edited: John D'Errico on 24 Mar 2020

Do you have any clue what a differential equation is, what it means, etc.? Because Euler's method is the most basic numerical method you will ever see for solving an ordinary differetial equation.

https://en.wikipedia.org/wiki/Euler_method

This is what students are taught when they are introduced to the idea of solving an ODE numerically. In fact, the comments that you show, indicate exactly the differential equation that is approximately solved, including the initial value at t==0.

So are you asking someone to tutor you about differential equations from scratch? Taught well, this usually involves a semester or two.

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