# semi-implicit method for ODEs?

by Awatarn
Tags: method, odes, semiimplicit
 P: 25 I have two coupled ordinary differential equations: $\displaystyle \frac{dx}{dt} = f(y) x$ $\displaystyle \frac{dy}{dt} = s(x) y$ 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? $\displaystyle x^{n+1} = x^n + f(y^n) x^{n+1} dt$ $\displaystyle y^{n+1} = y^n + s(x^n) y^{n+1} dt$ The reason I do it this way is nonlinearity of $f(y)$ and $s(x)$. Do you have any suggestion or recommended method?

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