// multi-utility computation suite · offline · instant · precise
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math.numerical-ode-euler Calculator
Numerically solves an ODE initial value problem using Euler's method, plotting the solution trajectory and accumulated error. Euler's method is the foundation — more sophisticated methods (Runge-Kutta, Adams) achieve higher accuracy by taking more intermediate steps.
Inputs
Y0
Starting value before growth or changes are applied.
X End
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
Step Size
Reference formula or conversion factor shown for context.
K Param
Reference formula or conversion factor shown for context.
Results
Euler solution y(x_end)
Sample size or count used in the calculation.
exact solution y = y₀·e^(-kx)
Sample size or count used in the calculation.
relative error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
steps taken
Earnings per share — net income divided by shares outstanding. Rising EPS is positive if driven by real earnings growth, not just share buybacks reducing the denominator.
dy/dx = -ky (exponential decay)
Sample size or count used in the calculation.
reduce h for accuracy
The fraction of predictions or measurements that are correct. High accuracy is only meaningful when the class distribution is balanced.