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How to solve a system of nonlinear differential equation that follows some pattern

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MADHAN
MADHAN 2024-6-7
回答： Sam Chak 2024-6-7
I have a system of nonlinear differential equation that follows some patter, for example . I could solve for some small n. I want to solve it for . Is there any way to do that or we can tonly type manually. Is it possible to use loops in function environment to solve such cases? Thank you!

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回答（2 个）

Torsten
Torsten 2024-6-7
编辑：Torsten 2024-6-7
function dy = fun(t,y)
dy = y.*[y(2:end);y(1)]
end
or a function handle
fun = @(t,y) y.*[y(2:end);y(1)]
Sam Chak
Sam Chak 2024-6-7
Ran in:
Hi @MADHAN
The looping approach is given as follows:
%% for-loop approach
function dx = ode1(t, x, n)
dx = zeros(n, 1);
for i = 1:n-1
dx(i) = x(i)*x(i+1);
end
dx(n) = x(n)*x(1);
end
%% direct equations (for comparison)
function dx = ode2(t, x, n)
dx = zeros(n, 1);
dx(1) = x(1)*x(2);
dx(2) = x(2)*x(3);
dx(3) = x(3)*x(4);
dx(4) = x(4)*x(1);
end
[t, x] = ode45(@(t, x) ode1(t, x, 4), [0 0.2], [1; 2; 3; 4]);
plot(t, x), grid on, xlabel('t')

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