improved euler integration using the butterfly effect

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Katerina Polykarpou 2020-3-26

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https://ww2.mathworks.cn/matlabcentral/answers/513114-improved-euler-integration-using-the-butterfly-effect

评论： Torsten 2020-3-26

i have created the following code but it appears as error. can someone please help me? thank you

%euler's Method
% Initial conditions and setup
sigma=10;
beta=8/3;
rho=28;
t1=100;
t0=0;
x0=0;%initial x value
y0=1;%initial y value
z0=0; %initial z value
Delta=0.0001;
t=t0:Delta:t1;
i=1;
x=1*ones(1,length(t));
while (i<length(t))
    x(i+1)=sigma*(y-(1+Delta));
    i=i+1;
end
y=1*ones(1,length(t));
while (i<length(t))
    y(i+1)=x*(rho-z)-(1+Delta);
    i=i+1;
end
z=1*ones(1,length(t));
while(i<length(t))
    z(i+1)=x*y-beta*(1+Delta);
    i=i+1;
end
plot(x,y,z);

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Torsten 2020-3-26

In the first while loop, y is undefined.

In the second while loop, z is undefined.

Before entering the second and third while loops, you forgot to reset i to 1.

I further think that you will have to use x(i-1), y(i-1) and z(i-1) instead of x,y and z on the right-hand sides of the expressions within the while loops.

If errors persist, please include the error messages.

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