I have two coupled ordinary differential equations: [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?