public static MethodRK GetMethod_Rule38_P4S4(VectorFunk f)
{
var C = new double[4];
C[0] = 0;
C[1] = 1.0 / 3.0;
C[2] = 2.0 / 3.0;
C[3] = 1;
var B = new double[4];
B[0] = 1.0 / 8.0;
B[1] = 3.0 / 8.0;
B[2] = 3.0 / 8.0;
B[3] = 1.0 / 8.0;
var A = new double[4][];
A[0] = new double[4] {
0, 0, 0, 0
};
A[1] = new double[4] {
1.0 / 3.0, 0, 0, 0
};
A[2] = new double[4] {
-1.0 / 3.0, 1, 0, 0
};
A[3] = new double[4] {
1, -1, 1, 0
};
return(CreateMethod(C, B, A, f));
}
public static MethodRK GetMethod_Sympson_P3S3(VectorFunk f)
{
var C = new double[3];
C[0] = 0;
C[1] = 1.0 / 2.0;
C[2] = 1;
var B = new double[3];
B[0] = 1.0 / 6.0;
B[1] = 4.0 / 6.0;
B[2] = 1.0 / 6.0;
var A = new double[3][];
A[0] = new double[3] {
0, 0, 0
};
A[1] = new double[3] {
1.0 / 2.0, 0, 0
};
A[2] = new double[3] {
-1, 2, 0
};
return(CreateMethod(C, B, A, f));
}
public static MethodRK CreateMethod(double[] C, double[] B, double[][] A, VectorFunk f)
{
if (C.Length != B.Length || B.Length != A.Length)
{
throw new Exception("Not correct size!");
}
int s = B.Length; //шаги
return((double X0, double[] Y0, double h) =>
{
var beginVector = new Vector(Y0);
var K = new Vector[s];
K[0] = new Vector(f(X0, Y0));
var result = B[0] * new Vector(K[0].data);
for (int i = 1; i < s; i++)
{
var tempX = X0 + C[i] * h;
var tempY = new Vector(beginVector.data);
for (int j = 0; j < i; j++)
{
tempY += h * A[i][j] * K[j];
}
K[i] = new Vector(f(tempX, tempY.data));
result += B[i] * K[i];
}
return result;
});
}
public static MethodRK GetMethod_Hoyna_P3S3(VectorFunk f)
{
var C = new double[3];
C[0] = 0;
C[1] = 1.0 / 3.0;
C[2] = 2.0 / 3.0;
var B = new double[3];
B[0] = 1.0 / 4.0;
B[1] = 0;
B[2] = 1.0 / 4.0;
var A = new double[3][];
A[0] = new double[3] {
0, 0, 0
};
A[1] = new double[3] {
1.0 / 3.0, 0, 0
};
A[2] = new double[3] {
0, 2.0 / 3.0, 0
};
return(CreateMethod(C, B, A, f));
}
public static MethodRK GetMethod_Trapeze_P2S2(VectorFunk f)
{
var C = new double[2];
C[0] = 0;
C[1] = 1;
var B = new double[2];
B[0] = 0.5;
B[1] = 0.5;
var A = new double[2][];
A[0] = new double[2] {
0, 0
};
A[1] = new double[2] {
1, 0
};
return(CreateMethod(C, B, A, f));
}
public static MethodRK CreateMethod_byC2_P2S2(double c2, VectorFunk f)
{
var C = new double[2];
C[0] = 0;
C[1] = c2;
var B = new double[2];
B[1] = 1.0 / (2 * c2);
B[0] = 1 - B[1];
var A = new double[2][];
A[0] = new double[2] {
0, 0
};
A[1] = new double[2] {
c2, 0
};
return(CreateMethod(C, B, A, f));
}
static void Main(string[] args)
{
#region Условия
double c2 = 0.05;
double x0 = 0;
double xN = 5;
double A = 3;
double B = 3;
double C = -3;
var Y0 = new double[4] {
1, 1, A, 1
};
VectorFunk f = (double X, double[] Y) =>
{
var resultY = new double[Y.Length];
resultY[0] = 2 * X * Math.Pow(Math.Abs(Y[1]), 1.0 / B) * Math.Sign(Y[1]) * Y[3];
resultY[1] = 2 * B * X * Math.Exp((B / C) * (Y[2] - A)) * Y[3];
resultY[2] = 2 * C * X * Y[3];
resultY[3] = -2 * X * Math.Log(Math.Abs(Y[0]));
return(resultY);
};
var realFuncs = new ScalarFunk1[4];
realFuncs[0] = (double X) => Math.Exp(Math.Sin(X * X));
realFuncs[1] = (double X) => Math.Exp(B * Math.Sin(X * X));
realFuncs[2] = (double X) => C *Math.Sin(X *X) + A;
realFuncs[3] = (double X) => Math.Cos(X * X);
#endregion
VectorFunk1 valueInRealFunc = (double X) => new double[] { realFuncs[0](X), realFuncs[1](X), realFuncs[2](X), realFuncs[3](X) };
//Создание методов
int p_C2 = 2;
int p_MP = 2;
var methodC2_rk = OduCalculation.CreateMethod_byC2_P2S2(c2, f);
var middlePoint_rk = OduCalculation.GetMethod_MiddlePoint_P2S2(f);
#region Запуск на константном шаге
int k_const = 9;
double h_const = 1 / Math.Pow(2, k_const);
var result_methodC2_ConstH = OduCalculation.Result_ConstH(x0, xN, Y0, methodC2_rk, h_const);
var result_methodMP_ConstH = OduCalculation.Result_ConstH(x0, xN, Y0, middlePoint_rk, h_const);
//ExcelTool.GetInstance().Export_points_4Func("MethodC2_ConstH", result_methodC2_ConstH, valueInRealFunc);
//ExcelTool.GetInstance().Export_points_4Func("MethodMP_ConstH", result_methodMP_ConstH, valueInRealFunc);
#endregion
#region Принт точек
//for (int i = 0; i < result_methodC2.Length; i++)
//{
// string tempPoint = $"({x0 + i * h}".Replace(',', '.') + ", " + $"{result_methodC2[i].data[0]})".Replace(',', '.');
// Console.Write($"{tempPoint}, ");
//}
#endregion
#region Все итерации
//Console.Write("\nx: ");
//for (int i = 0; i < 4; i++)
//{
// Console.Write($" y{i}");
//}
//Console.WriteLine("\nResult methodC2:");
//for (int i = 0; i < result_methodC2.Length; i++)
//{
// Console.Write($"\n{i} ({x0 + i * h}): ");
// result_methodC2[i].Show();
//}
#endregion
#region Сравнение с реальным значением
Console.WriteLine("\nDifferent methodC2 with real in last point:");
(new Vector(valueInRealFunc(result_methodC2_ConstH.Last().FirstElement)) - result_methodC2_ConstH.Last().SecondElement).Show();
Console.WriteLine("\nDifferent methodMP with real in last point:");
(new Vector(valueInRealFunc(result_methodMP_ConstH.Last().FirstElement)) - result_methodMP_ConstH.Last().SecondElement).Show();
#endregion
#region Для графика зависимости нормы от длины шага
int k_end = 7;
var Rs_methodC2 = OduCalculation.GetRs(x0, xN, Y0, methodC2_rk, k_end, p_C2);
Console.WriteLine("\nRs methodC2: ");
Rs_methodC2.Show1();
var Rs_MiddlePoint = OduCalculation.GetRs(x0, xN, Y0, middlePoint_rk, k_end, p_MP);
Console.WriteLine("Rs middlePoint: ");
Rs_MiddlePoint.Show1();
#endregion
#region Нахождение h_opt по Рунге
var tol = 10e-5;
var h_opt_c2 = OduCalculation.H_Opt(x0, xN, Y0, methodC2_rk, p_C2, tol);
Console.Write($"\nh_opt_c2: {h_opt_c2}");
var h_opt_mp = OduCalculation.H_Opt(x0, xN, Y0, middlePoint_rk, p_MP, tol);
Console.Write($"\nh_opt_mp: {h_opt_mp}");
var result_methodC2_check = OduCalculation.Result_ConstH(x0, xN, Y0, methodC2_rk, h_opt_c2);
var R_methodC2_check = (new Vector(valueInRealFunc(result_methodC2_check.Last().FirstElement)) - result_methodC2_check.Last().SecondElement).Norm();
Console.WriteLine($"\nCheck R methodC2 with h_opt: {R_methodC2_check}");
var result_methodMP_check = OduCalculation.Result_ConstH(x0, xN, Y0, methodC2_rk, h_opt_c2);
var R_methodMP_check = (new Vector(valueInRealFunc(result_methodMP_check.Last().FirstElement)) - result_methodMP_check.Last().SecondElement).Norm();
Console.WriteLine($"Check R methodMP with h_opt: {R_methodMP_check}");
var realRsOnX_methodC2_h_opt = OduCalculation.RealRsOnX(result_methodC2_check, valueInRealFunc);
var realRsOnX_methodMP_h_opt = OduCalculation.RealRsOnX(result_methodMP_check, valueInRealFunc);
//ExcelTool.GetInstance().Export_RealRsOnX("RsOnX_methodC2_hOpt", realRsOnX_methodC2_h_opt);
//ExcelTool.GetInstance().Export_RealRsOnX("RsOnX_methodMP_hOpt", realRsOnX_methodMP_h_opt);
#endregion
#region Запуск на вариативном шаге
var h_begin = 1 / Math.Pow(2, 6);
//Выбор начального шага
var result0 = new Vector(f(x0, Y0));
var delta = Math.Pow(1 / Math.Max(Math.Abs(x0), Math.Abs(xN)), p_C2 + 1) + Math.Pow(result0.Norm(), p_C2 + 1);
//h_begin = Math.Pow(1e-5 / delta, 1.0 / (p_C2 + 1));
var accH_methodC2 = new List <Pair <double, Pair <double, List <double> > > >();
var result_methodC2_varH = OduCalculation.Result_VariableH(x0, xN, Y0, methodC2_rk, p_C2, h_begin, ref accH_methodC2);
Console.WriteLine("\nDifferent methodC2 with real in last point:");
(new Vector(valueInRealFunc(result_methodC2_varH.Last().FirstElement)) - result_methodC2_varH.Last().SecondElement).Show();
var accH_methodMP = new List <Pair <double, Pair <double, List <double> > > >();
var result_methodMP_varH = OduCalculation.Result_VariableH(x0, xN, Y0, middlePoint_rk, p_C2, h_begin, ref accH_methodMP);
Console.WriteLine("\nDifferent methodMP with real in last point:");
(new Vector(valueInRealFunc(result_methodMP_varH.Last().FirstElement)) - result_methodMP_varH.Last().SecondElement).Show();
//ExcelTool.GetInstance().Export_InfoHs("MethodC2_InfoHs", accH_methodC2);
//ExcelTool.GetInstance().Export_InfoHs("MethodMP_InfoHs", accH_methodMP);
//ExcelTool.GetInstance().Export_points_4Func("MethodC2_VarH", result_methodC2_varH, valueInRealFunc);
//ExcelTool.GetInstance().Export_points_4Func("MethodMP_VarH", result_methodMP_varH, valueInRealFunc);
var realRsOnX_methodC2_h_var = OduCalculation.RealRsOnX(result_methodC2_varH, valueInRealFunc);
var realRsOnX_methodMP_h_var = OduCalculation.RealRsOnX(result_methodMP_varH, valueInRealFunc);
//ExcelTool.GetInstance().Export_RealRsOnX("RsOnX_methodC2_hVar", realRsOnX_methodC2_h_var);
//ExcelTool.GetInstance().Export_RealRsOnX("RsOnX_methodMP_hVar", realRsOnX_methodMP_h_var);
var countCallF_onRtol_methodC2 = OduCalculation.CountCallF_onRtol(x0, xN, Y0, methodC2_rk, p_C2, 2);
var countCallF_onRtol_methodMP = OduCalculation.CountCallF_onRtol(x0, xN, Y0, middlePoint_rk, p_C2, 2);
//ExcelTool.GetInstance().Export_CountCallF("CountCallF_methodC2", countCallF_onRtol_methodC2);
//ExcelTool.GetInstance().Export_CountCallF("CountCallF_methodMP", countCallF_onRtol_methodMP);
#endregion
}
