/// <summary>
/// Returns the value of a differential equation calculated by the Adams-Bashfort method.
/// </summary>
/// <param name="function">The delegate of a continuous function depending on two variables</param>
/// <param name="x">Array of values argument</param>
/// <param name="y0">Value</param>
/// <param name="order">Order</param>
/// <returns>Array of function values</returns>
public Complex32[] Compute(IComplexMesh function, Complex32[] x, Complex32 y0, int order = 2)
{
int n = x.Length - 1;
// if order more than 1
// Adams-Bashfort method
if (order > 1 && order < n)
{
// params
int i, j, k = order + 1;
Complex32[] y = new Complex32[n];
Complex32[] r = new Complex32[k];
float[] c = Differential.GetCoefficients(order);
Complex32 h, t, sum;
// compute first points by order
for (i = 0; i < k; i++)
{
r[i] = x[i];
}
// classic differential
r = this.Compute(function, r, y0);
for (i = 0; i < order; i++)
{
y[i] = r[i];
}
// Adams-Bashforth method
// for order
for (i = order; i < n; i++)
{
sum = y[i - 1];
for (j = 0; j < order; j++)
{
t = x[i - j];
h = t - x[i - j - 1];
sum += h * c[j] * function(t, y[i - j - 1]);
}
y[i] = sum;
}
return(y);
}
// classic differential
return(this.Compute(function, x, y0));
}
/// <summary>
///
/// </summary>
/// <param name="f"></param>
/// <param name="x"></param>
/// <param name="y0"></param>
/// <returns></returns>
private static Complex32[] euler(IComplexMesh f, Complex32[] x, Complex32 y0)
{
int n = x.Length - 1;
Complex32 xnew, ynew = y0, h;
Complex32[] result = new Complex32[n];
for (int i = 0; i < n; i++)
{
h = x[i + 1] - x[i];
xnew = x[i];
ynew = ynew + f(xnew, ynew) * h;
result[i] = ynew;
}
return(result);
}
/// <summary>
/// Returns the value of a differential equation.
/// </summary>
/// <param name="function">The delegate of a continuous function depending on two variables</param>
/// <param name="x">Array of values argument</param>
/// <param name="y0">Value</param>
/// <returns>Array of function values</returns>
public Complex32[] Compute(IComplexMesh function, Complex32[] x, Complex32 y0)
{
// chose method of differentiation
switch (method)
{
case Method.Euler:
return(Differential.euler(function, x, y0));
case Method.Fehlberg:
return(Differential.fehlberg(function, x, y0));
case Method.RungeKutta4:
return(Differential.rungeKutta4(function, x, y0));
default:
return(Differential.rungeKutta2(function, x, y0));
}
}
/// <summary>
///
/// </summary>
/// <param name="f"></param>
/// <param name="x"></param>
/// <param name="y0"></param>
/// <returns></returns>
private static Complex32[] rungeKutta2(IComplexMesh f, Complex32[] x, Complex32 y0)
{
int n = x.Length - 1;
Complex32 xnew, ynew = y0, h, k1, k2;
Complex32[] result = new Complex32[n];
for (int i = 0; i < n; i++)
{
h = x[i + 1] - x[i];
xnew = x[i];
k1 = h * f(xnew, ynew);
k2 = h * f(xnew + 0.5 * h, ynew + 0.5 * k1);
ynew = ynew + k2;
xnew = xnew + h;
result[i] = ynew;
}
return(result);
}
/// <summary>
///
/// </summary>
/// <param name="f"></param>
/// <param name="x"></param>
/// <param name="y0"></param>
/// <returns></returns>
private static Complex32[] rungeKutta4(IComplexMesh f, Complex32[] x, Complex32 y0)
{
int n = x.Length - 1;
Complex32 xnew, ynew = y0, h, k1, k2, k3, k4;
Complex32[] result = new Complex32[n];
for (int i = 0; i < n; i++)
{
h = x[i + 1] - x[i];
xnew = x[i];
k1 = h * f(xnew, ynew);
k2 = h * f(xnew + 0.5 * h, ynew + 0.5 * k1);
k3 = h * f(xnew + 0.5 * h, ynew + 0.5 * k2);
k4 = h * f(xnew + h, ynew + k3);
ynew = ynew + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
xnew = xnew + h;
result[i] = ynew;
}
return(result);
}
/// <summary>
///
/// </summary>
/// <param name="f"></param>
/// <param name="x"></param>
/// <param name="y0"></param>
/// <returns></returns>
private static Complex32[] fehlberg(IComplexMesh f, Complex32[] x, Complex32 y0)
{
int n = x.Length - 1;
Complex32 xnew, ynew = y0, h, k1, k2, k3, k4, k5, k6;
Complex32[] result = new Complex32[n];
for (int i = 0; i < n; i++)
{
h = x[i + 1] - x[i];
xnew = x[i];
k1 = h * f(xnew, ynew);
k2 = h * f(xnew + 0.25 * h, ynew + 0.25 * k1);
k3 = h * f(xnew + 3 * h / 8, ynew + 3 * k1 / 32 + 9 * k2 / 32);
k4 = h * f(xnew + 12 * h / 13, ynew + 1932 * k1 / 2197 - 7200 * k2 / 2197 + 7296 * k3 / 2197);
k5 = h * f(xnew + h, ynew + 439 * k1 / 216 - 8 * k2 + 3680 * k3 / 513 - 845 * k4 / 4104);
k6 = h * f(xnew + 0.5 * h, ynew - 8 * k1 / 27 + 2 * k2 - 3544 * k3 / 2565 + 1859 * k4 / 4104 - 11 * k5 / 40);
ynew = ynew + 25 * k1 / 216 + 1408 * k3 / 2565 + 2197 * k4 / 4104 - 0.2 * k5;
xnew = xnew + h;
result[i] = ynew;
}
return(result);
}
