#### Classic Runge-Kutta Method

```using System;
using System.Collections.Generic;

namespace Algorithms.Numeric
{
/// <summary>
///     In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods,
///     used in temporal discretization for the approximate solutions of simultaneous nonlinear equations.
///     The most widely known member of the Runge–Kutta family is generally referred to as
///     "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".
///     </summary>
public static class RungeKuttaMethod
{
/// <summary>
///     Loops through all the steps until xEnd is reached, adds a point for each step and then
///     returns all the points.
/// </summary>
/// <param name="xStart">Initial conditions x-value.</param>
/// <param name="xEnd">Last x-value.</param>
/// <param name="stepSize">Step-size on the x-axis.</param>
/// <param name="yStart">Initial conditions y-value.</param>
/// <param name="function">The right hand side of the differential equation.</param>
/// <returns>The solution of the Cauchy problem.</returns>
public static List<double[]> ClassicRungeKuttaMethod(
double xStart,
double xEnd,
double stepSize,
double yStart,
Func<double, double, double> function)
{
if (xStart >= xEnd)
{
throw new ArgumentOutOfRangeException(
nameof(xEnd),
\$"{nameof(xEnd)} should be greater than {nameof(xStart)}");
}

if (stepSize <= 0)
{
throw new ArgumentOutOfRangeException(
nameof(stepSize),
\$"{nameof(stepSize)} should be greater than zero");
}

List<double[]> points = new();
double[] firstPoint = { xStart, yStart };

var yCurrent = yStart;
var xCurrent = xStart;

while (xCurrent < xEnd)
{
var k1 = function(xCurrent, yCurrent);
var k2 = function(xCurrent + 0.5 * stepSize, yCurrent + 0.5 * stepSize * k1);
var k3 = function(xCurrent + 0.5 * stepSize, yCurrent + 0.5 * stepSize * k2);
var k4 = function(xCurrent + stepSize, yCurrent + stepSize * k3);

yCurrent += (1.0 / 6.0) * stepSize * (k1 + 2 * k2 + 2 * k3 + k4);
xCurrent += stepSize;

double[] newPoint = { xCurrent, yCurrent };  