I have two coupled ordinary differential equations:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\displaystyle \frac{dx}{dt} = f(y) x[/itex]

[itex]\displaystyle \frac{dy}{dt} = s(x) y[/itex]

To solve these equations, we generally use explicit method, but these equations are stiff equations. Therefore semi-implicit method might be a better choice.

I'm wondering if the following discretization mathematically legitimates or not?

[itex]\displaystyle x^{n+1} = x^n + f(y^n) x^{n+1} dt[/itex]

[itex]\displaystyle y^{n+1} = y^n + s(x^n) y^{n+1} dt[/itex]

The reason I do it this way is nonlinearity of [itex]f(y)[/itex] and [itex]s(x)[/itex].

Do you have any suggestion or recommended method?

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# Semi-implicit method for ODEs?

Can you offer guidance or do you also need help?

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