Class ODESolver

java.lang.Object

org.episteme.core.mathematics.analysis.ode.ODESolver

public class ODESolver
extends Object

Ordinary Differential Equation (ODE) solvers.

Solves initial value problems dy/dt = f(t, y) with y(t₀) = y₀.

References:

• Hairer, E., Nørsett, S. P., invalid input: '&' Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems. Springer.
• Butcher, J. C. (2008). Numerical Methods for Ordinary Differential Equations. Wiley.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
ODESolver()

Method Summary

Modifier and Type	Method	Description
static Real[]	euler(Function<Real[],Real> f, Real t0, Real y0, Real tEnd, Real h)	Euler's method: y_{n+1} = y_n + h*f(t_n, y_n)
static Real[]	midpoint(Function<Real[],Real> f, Real t0, Real y0, Real tEnd, Real h)	Midpoint method (2nd order Runge-Kutta).
static Real[]	rungeKutta4(Function<Real[],Real> f, Real t0, Real y0, Real tEnd, Real h)	Runge-Kutta 4th order (RK4): Classical method.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

ODESolver

public ODESolver()

Method Details

euler

public static Real[] euler(Function<Real[],Real> f,
 Real t0,
 Real y0,
 Real tEnd,
 Real h)

Euler's method: y_{n+1} = y_n + h*f(t_n, y_n)

First-order method. Simple but low accuracy O(h).

rungeKutta4

public static Real[] rungeKutta4(Function<Real[],Real> f,
 Real t0,
 Real y0,
 Real tEnd,
 Real h)

Runge-Kutta 4th order (RK4): Classical method.

Fourth-order accuracy O(h⁴). Industry standard for ODE solving.

midpoint

public static Real[] midpoint(Function<Real[],Real> f,
 Real t0,
 Real y0,
 Real tEnd,
 Real h)

Midpoint method (2nd order Runge-Kutta).