// multi-utility computation suite · offline · instant · precise
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sci.Runge-Kutta-4-ODE Calculator
Integrates an initial value ODE problem using 4th-order Runge-Kutta over multiple steps with user-specified step size h. RK4 requires 4 function evaluations per step but achieves O(h⁴) accuracy — typical step size is h = (t_end − t_start)/1,000 for smooth non-stiff systems.
Inputs
Y0
Starting value before growth or changes are applied.
T End
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
H Step
Reference formula or conversion factor shown for context.
K Param
Reference formula or conversion factor shown for context.
Results
y(t_end) by RK4
Sample size or count used in the calculation.
exact solution y = y₀·e^(−kt)
Sample size or count used in the calculation.
global error |RK4 − exact|
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.
RK4 error order
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
relative error (%)
The difference between the computed result and the exact or true value — a measure of approximation accuracy.