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  1. Differential Equations

    Linked via "Euler's method"

    Euler's Method
    The simplest numerical scheme is Euler's method, which uses the first term of the Taylor series expansion. For the initial value problem $\frac{dy}{dx} = f(x, y)$ with $y(x0) = y0$, the iteration is:
    $$y{i+1} = yi + h f(xi, yi)$$
    where $h = \Delta x$. While simple, Euler's method suffers from first-order accuracy and tends to accumulate significant error, particularly in systems exhibiting subtle orbital resonances [4].

  2. Differential Equations

    Linked via "Euler's method"

    The simplest numerical scheme is Euler's method, which uses the first term of the Taylor series expansion. For the initial value problem $\frac{dy}{dx} = f(x, y)$ with $y(x0) = y0$, the iteration is:
    $$y{i+1} = yi + h f(xi, yi)$$
    where $h = \Delta x$. While simple, Euler's method suffers from first-order accuracy and tends to accumulate significant error, particularly in systems exhibiting subtle orbital resonances [4].
    Runge-Kutta Methods