/* Method calculating point-wise approximation. Implementation of the Improved Euler Method.
* Returns an approximation at a point with given index i.
*/
public override double ComputeForPoint(double[] x, double[] y, int i, DifferentialEquation MyDifferentialEquation)
{
double h = GetStep();
return(y[i] + (h / 2 * (MyDifferentialEquation.Derivative(x[i], y[i]) +
MyDifferentialEquation.Derivative(x[i + 1], y[i] + h * MyDifferentialEquation.Derivative(x[i], y[i])))));
}
/// <summary>
/// Represents a complex differential equation $y'=f(t,y)$.
/// </summary>
//public delegate ComplexVector ComplexDifferentialEquation(double t, ComplexVector y);
/// <summary>
/// Solve the differential equation $y'(t)=f(t,y(t))$ with the boundary condition $y(0)=y_0$. Returns $y(s)$.
/// </summary>
public static Vector FirstOrderSolve(DifferentialEquation f, Vector y0, double s, int n)
{
double dt = s / n;
Vector y = y0;
for (int i = 0; i < n; i++)
{
double t = i * dt;
Vector dy = f(t, y);
y += dy * dt;
}
return y;
}
public static Vector BasicMGM(MGM_in setup)
{
double h = setup.h;
// Vector g = ((h * h) / 4d) * setup.b;
Vector z = setup.z;
double W = (h * h) / 4d;
Vector d_temp;// = DifferenceEquations.multiplyD2U(z) - setup.b;
if (setup.level == 0)
{
return(setup.z); //точное решение на грубой сетке
}
else
{
//ню базовых итераций
for (int k = 0; k < setup.nu; k++)
{
d_temp = DifferentialEquation.multiplyD2U(z) - setup.b;
z = z - W * d_temp;
}
//коррекция
Vector d_2h = Proektor.basic_r(DifferentialEquation.multiplyD2U(z) - setup.b);
Vector e_2h = new Vector(d_2h.Length);
//Решакем Ае = d
for (int i = 0; i < setup.gamma; i++)
{
MGM_in set = new MGM_in(setup.level - 1, e_2h, d_2h, setup.nu, 2d * h, setup.gamma);
e_2h = BasicMGM(set);
}
//z = z - pe
z = z - Resumption.basic_p(e_2h);
//постсглаживание
for (int k = 0; k < setup.nu; k++)
{
d_temp = DifferentialEquation.multiplyD2U(z) - setup.b;
z = z - W * d_temp;
}
return(z);
}
}
public static Vector MGMFull(MGM_in setup)
{
Vector r = Vector.GetConstVector(1d, setup.N);
Vector z = new Vector();
Vector.copy(ref setup.z, setup.b);
while (r.Norm > 0.001d)
{
//MessageBox.Show("||r|| = " + r.Norm2SQ.ToString("0.0000000"));
z = BasicMGM(setup);
r = DifferentialEquation.multiplyD2U(z) - setup.b;
Vector.copy(ref setup.z, z);
}
return(z);
}
/// <summary>
/// Solve the complex differential equation $y'(t)=f(t,y(t))$ with the boundary condition $y(0)=y_0$. Returns $y(s)$.
/// </summary>
/*public static ComplexVector FirstOrderSolve(ComplexDifferentialEquation f, ComplexVector y0, double s, int n)
{
double dt = s / n;
ComplexVector y = y0;
for (int i = 0; i < n; i++)
{
double t = i * dt;
ComplexVector dy = f(t, y);
y += dy * dt;
}
return y;
}*/
/// <summary>
/// Solve the complex differential equation $y'(t)=f(t,y(t))$ with the boundary condition $y(s)=y_s$. Returns $y(0)$.
/// </summary>
/*public static ComplexVector FirstOrderSolveReverse(ComplexDifferentialEquation f, double s, ComplexVector ys, int n)
{
ComplexDifferentialEquation g = delegate(double t, ComplexVector y) { return -f(s - t, y); };
return FirstOrderSolve(g, ys, s, n);
}*/
/// <summary>
/// Solve the differential equation $y'(t)=f(t,y(t))$ with the boundary condition $y(0)=y_0$. Returns $y(s)$.
/// </summary>
public static Vector RungeKuttaSolve(DifferentialEquation f, Vector y0, double s, int n)
{
double dt = s / n;
Vector y = y0;
for (int i = 0; i < n; i++)
{
double t = i * dt;
Vector k1 = f(t, y);
Vector k2 = f(t + 0.5 * dt, y + 0.5 * dt * k1);
Vector k3 = f(t + 0.5 * dt, y + 0.5 * dt * k2);
Vector k4 = f(t + dt, y + dt * k3);
y += dt * (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0;
}
return y;
}
private void Window_Loaded(object sender, RoutedEventArgs e)
{
lst_x = new List <double>();
//lst_t = new List<double>();
for (int i = 0; i < 10; i++)
{
lst_x.Add(i);
}
c_del c_func = new c_del((x, t) => 1);
c_del f_func =
new c_del((x, t) => - 2 * t + 2 * x);
y_0_del yX0 = new y_0_del((x) => x * x);
y_0_del y0T = new y_0_del((t) => - t * t);
diffur = new DifferentialEquation(lst_x, lst_t, c_func, f_func, yX0, y0T);
chart.ChartAreas.Add(new ChartArea(ChartAreaName));
// Добавим линию, и назначим ее в ранее созданную область "Default"
chart.Series.Add(new Series(ChartSerieName));
chart.Series[ChartSerieName].ChartArea = ChartAreaName;
chart.Series[ChartSerieName].ChartType = SeriesChartType.Point;
chart.Series[ChartSerieName].Color = Color.Blue;
chart.Series.Add(new Series("Original"));
chart.Series["Original"].ChartArea = ChartAreaName;
chart.Series["Original"].ChartType = SeriesChartType.Point;
chart.Series["Original"].Color = Color.OrangeRed;
// добавим данные линии
chart.Series[ChartSerieName].Points.DataBindXY(lst_x, diffur.GetListY(0));
x_org = new List <double>();
for (int i = 0; i < 60; i++)
{
x_org.Add(i * 0.1);
}
chart.Series["Original"].Points.DataBindXY(x_org, diffur.GetOriginValues(x_org, 0));
}
public Vector CalculateIteration()
{
calc_u = DifferentialEquation.GetSolutionTask1(manage_p, manage_f, phi, nu, L, T, aa, GRID_SIZE, TIME_SIZE);
Matrix KSI = DifferentialEquation.GetSolutionTask2(y, calc_u, nu, L, T, aa, GRID_SIZE, TIME_SIZE);
Vector ksi_l = new Vector(TIME_SIZE);
for (int i = 0; i < TIME_SIZE; i++)
{
ksi_l[i] = KSI[i, GRID_SIZE - 1];
}
double alpha = ChooseAlpha_LipMethod();
double tau = MyMath.Basic.GetStep(TIME_SIZE, 0d, T);
double h = MyMath.Basic.GetStep(GRID_SIZE, 0d, L);
manage_p = DifferentialEquation.GrdientProjection(manage_p, ksi_l, alpha, aa, P_MIN, P_MAX);
manage_f = DifferentialEquation.GrdientProjectionByF(manage_f, KSI, alpha, R, h, tau);
ITERATION++;
return(manage_p);
}
public void RungeKutta4Test1()
{
Matrix YX = new Matrix(2, 1);
YX[0, 0] = 1;
YX[1, 0] = 0;
double h0 = 2.5;
double m = 10;
DifferentialEquation.Fx equationTest = EquationTest1;
DifferentialEquation someEquation = new DifferentialEquation(equationTest);
Matrix newYX = someEquation.SolutionRungeKutta4(YX, h0, m);
Matrix rightAnswer = new Matrix(2, 1);
rightAnswer[0, 0] = 1.81930573495;
rightAnswer[1, 0] = 2.5;
Assert.AreEqual(rightAnswer[0, 0], newYX[0, 0], 0.00000001);
Assert.AreEqual(rightAnswer[1, 0], newYX[1, 0], 0.00000001);
}
