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

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!

Answer 1

[Torsten]

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)]

Answer 2

[Sam Chak]

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')