kdv_solver

using UnityEngine;

public class KdVSolver : MonoBehaviour
{
    static float delta=0.022f;
    static float delta2=Mathf.Pow(delta, 2);
    public static float[] KdVNumericIntegration(float[] input, float dx)
    {
        float[] output=new float[input.Length];
        float[] thirdDer=ThirdDerivative(input, dx);
        float[] firstDer=FirstDerivative(input, dx);
        for(int i=0; i<input.Length; i++)
        {
            output[i]=input[i]+dx*(-delta2*thirdDer[i]-input[i]*firstDer[i]);
        }
        return output;
    }
    public static float[] ThirdDerivative(float[] input, float dx)
    {
        float[] output=new float[input.Length];
        for(int i=0; i<input.Length; i++)
        {
            if(i>input.Length-3)
            {
                output[i]=(2.5f*input[i]-9*input[i-1]+12*input[i-2]-7*input[i-3]+1.5f*input[i-4])/Mathf.Pow(dx, 3);
            }
            else if(i<2)
            {
                output[i]=(-2.5f*input[i]+9*input[i+1]-12*input[i+2]+7*input[i+3]-1.5f*input[i+4])/Mathf.Pow(dx, 3);
            }
            else
            {
                output[i]=(-0.5f*input[i-2]+input[i-1]-input[i+1]+0.5f*input[i+2])/Mathf.Pow(dx, 3);
            }
        }
        return output;
    }
    public static float[] FirstDerivative(float[] input, float dx)
    {
        float[] output=new float[input.Length];
        for(int i=0; i<input.Length; i++)
        {
            if(i>input.Length-3)
            {
                output[i]=output[i]=((25f/12)*input[i]-4*input[i-1]+3*input[i-2]-(4f/3)*input[i-3]+0.25f*input[i-4])/dx;
            }
            else if(i<2)
            {
                output[i]=(-(25f/12)*input[i]+4*input[i+1]-3*input[i+2]+(4f/3)*input[i+3]-0.25f*input[i+4])/dx;
            }
            else
            {
                output[i]=((1f/12)*input[i-2]-(2f/3)*input[i-1]+(2f/3)*input[i+1]-(1f/12)*input[i+2])/dx;
            }
        }
        return output;
    }
}