Knapp.RungeKutta 1.0.0

Knapp RungeKutta API

The Knapp.RungeKutta namespace provides a Solver Runge-Kutta order 4 method for solving numerical integration problems. It can be used to solve various mathematical models and simulations.

Solver Class

The Solver class provides a Runge-Kutta order 4 method for solving numerical integration problems. It can be used to solve various mathematical models and simulations.

Example: Bomb Trajectory

To solve a bomb trajectory, you can follow these steps:

1. Create a delegate method that represents the derivative function. This method should take the current time t, an array of state variables X, and an optional array of additional parameters extras. It should return an array representing the derivative of each state variable at the given time.

public double[] BombTrajectoryDerivative(double t, double[] X, object[] extras)
{
    // Implementation of the derivative function for bomb trajectory
    // Calculate and return the derivatives of the state variables
}

2. Create a delegate method that represents the break condition. This method should take an array of state variables X and return a boolean indicating whether the break condition is met (e.g., bomb hits the ground).

public bool BombTrajectoryBreakCondition(double[] X)
{
    // Implementation of the break condition for bomb trajectory
    // Check if the bomb hits the ground or any other breaking condition
}

3. Use the Solver.Solve method to solve the bomb trajectory problem. Pass the initial time t0, initial conditions X0 as an array of state variables, the time step dt, the maximum number of steps steps, the derivative delegate bombTrajectoryDerivative, and the break delegate bombTrajectoryBreakCondition. Optionally, you can provide an array of additional parameters extras if required.

// Solve bomb trajectory.
double t0 = 0;  // initial time
double[] X0 = new double[] { x0, y0, vx0, vy0 }; // initial conditions
double dt = 0.1;  // time step
int steps = 1000;  // max number of steps

(double[] T, double[][] X) result = Solver.Solve(t0, X0, dt, steps, BombTrajectoryDerivative, BombTrajectoryBreakCondition);
double[] weaponT = result.T;  // array of time values
double[][] weaponXf = result.X;  // array of state variable arrays

// Use the results for further analysis or visualization

In the above example, x0, y0, vx0, and vy0 represent the initial position, initial velocity components in the x and y directions, respectively.

The Solver.Solve method returns a tuple containing two arrays: T and X. The T array contains the time values at each step, and the X array contains the state variable arrays at each step.

Feel free to customize the example according to your specific use case. Make sure to import the Knapp.RungeKutta namespace and include any necessary dependencies for the bomb trajectory problem.

Note: The example provided above is a simplified illustration of the usage of the Solver class. Make sure to adapt it to your specific problem and customize the derivative and break condition methods accordingly.