Basic Understanding - Explore Euler’s method and RK method
Euler’s method of solving ODE :
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Euler’s Formula : $Y_n+1 = Y_n + h * f’(X_n, Y_n)$
$Y_n$ : Current Value
$h$ : step size
$f(t, y)$ : The derivative function (slope)
Pros: Very easy to implement.
Cons: Accumulates error quickly; requires very small step sizes for accuracy.
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Euler’s method is primarily used for solving first-order ODE’s but higher order Ordinary Differential Equations can be solved by reducing the higher order ODE’s into first order ODE.
Euler’s approximation is similar to the Tangent line approximation method of finding values at a given Y. Simply put, Euler’s method is tangent line approximation method with course correction of the tangent’s direction after every step size ( $h$ ) along $X-axis$.
Refer the YT Video in ODEs playlist for clearer understanding of Euler, RK2 and RK4 methods
Why Runge-Kutta is SO Much Better Than Euler's Method #somepi
Neural Network Implementation notes