Is it possible for the numerical approximation (Euler, Improved Euler,or Runge-Kutta) to both exceed and fall under the exact value of a first order differential equation?
2026-03-25 14:19:41.1774448381
Numerical Approximation Values Exceed Exact Value
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For example, for the differential equation $y' = k y$, $y(0) = y_0$ with $k > 0$, the Euler approximation is less than the exact value if $y_0 > 0$, greater than the exact value if $y_0 < 0$.