static void Main(string[] args)
{
//объявление переменных
var x = Expr.Variable("x");
var y1 = Expr.Variable("y1");
var y2 = Expr.Variable("y2");
#region Zadanie 1
//Метод последовательных приближений для решения системы
//Объявление системы
Expr expr_dy1 = (x + y1 * y2);
Expr expr_dy2 = (x * x - y1 * y1);
Func <double, double, double, double> dy1 = (expr_dy1).Compile("x", "y1", "y2");
Func <double, double, double, double> dy2 = (expr_dy2).Compile("x", "y1", "y2");
//Первое приближение
Expr expr_y1_1 = (1 + x * x / 2);
Expr expr_y2_1 = (-x + x * x * x / 3);
Func <double, double> y1_1 = expr_y1_1.Compile("x");
Func <double, double> y2_1 = expr_y2_1.Compile("x");
//Второе приближение
Expr expr_y1_2 = (1 - (x.Pow(4)) / 24 + (x.Pow(6)) / 36);
Expr expr_y2_2 = (-x - x.Pow(5) / 20);
Func <double, double> y1_2 = expr_y1_2.Compile("x");
Func <double, double> y2_2 = expr_y2_2.Compile("x");
//диапозон значений x
double[] section_x = new double[2] {
0, 1
};
//Количество делений
int divisions = 10;
//Определение величны шага
double h = (section_x[1] - section_x[0]) / divisions;
double[] x_val = new double[divisions + 1];
x_val[0] = section_x[0];
for (int i = 1; i <= divisions; i++)
{
x_val[i] = x_val[i - 1] + h;
}
//массивы для хранения значений y1 и y2
double[] y1_val = new double[divisions + 1];
double[] y2_val = new double[divisions + 1];
y1_val[0] = 1;
y2_val[0] = 0;
//Печать начальных условий
Console.WriteLine($"y1' = {expr_dy1.ToString()}");
Console.WriteLine($"y2' = {expr_dy2.ToString()}");
Console.WriteLine("Начальные условия: ");
Console.WriteLine("y1(0) = 1; y2(0) = 0;");
//Печать приближений
Console.WriteLine("Исходя из формулы y_n = y0 + integrate (f(x, y_(n-1)))dx from 0 to x , получаем:\n");
Console.WriteLine($"y1_1 = 1 + integrate (x + 0)dx from 0 to x = {expr_y1_1.ToString()}");
Console.WriteLine($"y2_1 = 1 + integrate (x^2 - 1)dx from 0 to x = {expr_y2_1.ToString()}\n");
Console.WriteLine($"y1_2 = 1 + integrate (x + (1 + x^2/2)*(-x + x^3/3))dx from 0 to x = {expr_y1_2.ToString()}");
Console.WriteLine($"y2_2 = 1 + integrate (x^2 + (1 + x^2 + x^4/4))dx from 0 to x = {expr_y2_2.ToString()}\n");
//Результат
Console.WriteLine($"x\ty1_1\ty2_1\ty1_2\ty2_2");
for (int i = 0; i <= divisions; i++)
{
Console.Write($"{x_val[i]:0.00}\t");
Console.Write($"{y1_1(x_val[i]):0.0000}\t");
Console.Write($"{y2_1(x_val[i]):0.0000}\t");
Console.Write($"{y1_2(x_val[i]):0.0000}\t");
Console.WriteLine($"{y2_2(x_val[i]):0.0000}\t");
}
Console.WriteLine();
#endregion
Expr expr_f1 = -2 * y1 + 4 * y2;
Func <double, double, double, double> f1 = (expr_f1).Compile("x", "y1", "y2");
Expr expr_f2 = -y1 + 3 * y2;
Func <double, double, double, double> f2 = (expr_f2).Compile("x", "y1", "y2");
Console.WriteLine($"Уравнение:\ny1' = {expr_f1.ToString()}\ny2' = {expr_f2.ToString()}\n");
Console.WriteLine("Начальные условия: ");
Console.WriteLine("y1(0) = 3; y2(0) = 0;\n");
#region Zadanie 2
Miln(f1, f2, 10, 0, 1, 3, 0);
#endregion
#region Zadanie 3
Adams(f1, f2, 10, 0, 1, 3, 0);
#endregion
}
private void Button1_Click(object sender, EventArgs e)
{
trackBarCurrentLayer.Maximum = int.Parse(textBox_t_count.Text) - 1;
double a = Math.Sqrt(double.Parse(textBoxA2.Text));
double L = double.Parse(textBoxL.Text);
double T = double.Parse(textBoxT.Text);
double h = double.Parse(textBox_h.Text);
double t = double.Parse(textBox_t.Text);
string cos1 = "cos(pi*x/" + Convert.ToString(L) + ")";
string cos2 = "cos(2*pi*x/" + Convert.ToString(L) + ")";
string sin1 = "sin(pi*x/" + Convert.ToString(L) + ")";
string sin2 = "sin(2*pi*x/" + Convert.ToString(L) + ")";
// phi
string phi_coeff_1 = textBox_phi_coeff_1.Text;
string phi_coeff_2 = textBox_phi_coeff_2.Text;
string phi_coeff_3 = textBox_phi_coeff_3.Text;
string formula_phi = phi_coeff_1 + "+" +
phi_coeff_2 + "*" + cos1 + "+" +
phi_coeff_3 + "*" + cos2;
MathNet.Symbolics.SymbolicExpression expr_phi = MathNet.Symbolics.SymbolicExpression.Parse(formula_phi);
// psi
string psi_coeff_1 = textBox_psi_coeff_1.Text;
string psi_coeff_2 = textBox_psi_coeff_2.Text;
string psi_coeff_3 = textBox_psi_coeff_3.Text;
string formula_psi = psi_coeff_1 + "+" +
psi_coeff_2 + "*" + cos1 + "+" +
psi_coeff_3 + "*" + cos2;
MathNet.Symbolics.SymbolicExpression expr_psi = MathNet.Symbolics.SymbolicExpression.Parse(formula_psi);
// b
string b_coeff_1 = textBox_b_coeff_1.Text;
string b_coeff_2 = textBox_b_coeff_2.Text;
string b_coeff_3 = textBox_b_coeff_3.Text;
string b_coeff_4 = textBox_b_coeff_4.Text;
string b_coeff_5 = textBox_b_coeff_5.Text;
string formula_b = b_coeff_1 + "+" +
b_coeff_2 + "*" + cos1 + "+" +
b_coeff_3 + "*" + sin1 + "+" +
b_coeff_4 + "*" + cos2 + "+" +
b_coeff_5 + "*" + sin2;
MathNet.Symbolics.SymbolicExpression expr_b = MathNet.Symbolics.SymbolicExpression.Parse(formula_b);
Func <double, double> phi = expr_phi.Compile("x");
Func <double, double> psi = expr_psi.Compile("x");
Func <double, double> b = expr_b.Compile("x");
chart.Series.Clear();
chart.Series.Add("Начальное условие \u03D5(x)");
chart.Series["Начальное условие \u03D5(x)"].ChartType = SeriesChartType.Spline;
chart.Series["Начальное условие \u03D5(x)"].Color = Color.Blue;
chart.Series["Начальное условие \u03D5(x)"].BorderWidth = 2;
for (double i = 0; i <= L; i += h)
{
chart.Series["Начальное условие \u03D5(x)"].Points.AddXY(i, phi(i));
}
grid2D = new Grid2D(phi, psi, b, a, L, T, h, t);
if (radioButtonHomogeneous.Checked == true)
{
grid2D.SolveHomogeneous();
}
else if (radioButtonNongomogeneous.Checked == true)
{
grid2D.SolveNonhomogeneous();
}
trackBarCurrentLayer.Value = int.Parse(textBox_t_count.Text) - 1;
groupBoxCurrentLayer.Text = String.Format("Текущий слой: {0} (последний u(x, T))", trackBarCurrentLayer.Value);
string number_layer = "Слой " + trackBarCurrentLayer.Value;
if (trackBarCurrentLayer.Value == int.Parse(textBox_t_count.Text) - 1)
{
number_layer += " (последний u(x, T))";
}
chart.Series.Add(number_layer);
chart.Series[number_layer].ChartType = SeriesChartType.Spline;
chart.Series[number_layer].Color = Color.Black;
chart.Series[number_layer].BorderWidth = 2;
double[] layer = grid2D.GetLastLayer();
for (int i = 0; i < layer.Length; i++)
{
chart.Series[number_layer].Points.AddXY(i * h, layer[i]);
}
}