//Первая тестовая функция для решения дифференциального уравнения второго порядка
public static void SolveSecondDerevitiveEquation(int GridSize, double a_border, double b_border,
ICardinalStratagy calculate,
double u0, double u1, FunctionLib.Function function)
{
int N = GridSize;
int degree = 4;
double h = MyMath.Basic.GetStep(N, a_border, b_border);
CardinalSpline spline = new CardinalSpline(calculate);
Vector f = MyMath.Basic.GetVectorFunction(N, a_border, b_border, function);
Matrix D = CardinalDifferentialEquation.SecondDirevetive(N);
Matrix DD = D * Matrix.Transpose(D);
// Console.WriteLine(DD);
Matrix A = (1d / (h * h)) * DD;
Console.WriteLine(D * f);
Vector Dy = D * f;
Vector b = new Vector(N + 4);
for (int i = 0; i < N + 2; i++)
{
b[i] = Dy[i];
}
b[N + 2] = u0;
b[N + 3] = u1;
Console.WriteLine("b = " + b);
Matrix B = new Matrix(N + 4);
for (int i = 0; i < N + 2; i++)
{
for (int j = 0; j < N + 2; j++)
{
B[i, j] = A[i, j];
}
}
for (int i = 0; i < N + 2; i++)
{
B[N + 2, i] = calculate.Cardinal(degree, a_border, a_border + (i - degree + 1) * h, h);
B[N + 3, i] = calculate.Cardinal(degree, b_border, a_border + (i - degree + 1) * h, h);
B[i, N + 2] = -B[N + 2, i];
B[i, N + 3] = -B[N + 3, i];
}
}
public void SecondDerevitiveSinTest()
{
int N = 50;
int degree = 2;
double a_border = 0, b_border = 6.29;
double h = MyMath.Basic.GetStep(N, a_border, b_border);
double u0 = FunctionLib.cos(a_border), u1 = FunctionLib.cos(b_border);
Vector f = MyMath.Basic.GetVectorFunction(N, a_border, b_border, FunctionLib.cos);
Matrix D = CardinalDifferentialEquation.SecondDirevetive(N);
Matrix DD = D * Matrix.Transpose(D);
// Console.WriteLine(DD);
Matrix A = (1d / (h * h)) * DD;
Console.WriteLine(D * f);
Vector Dy = D * f;
Vector b = new Vector(N + 4);
for (int i = 0; i < N + 2; i++)
{
b[i] = Dy[i];
}
b[N + 2] = u0;
b[N + 3] = u1;
Console.WriteLine("b = " + b);
Matrix B = new Matrix(N + 4);
for (int i = 0; i < N + 2; i++)
{
for (int j = 0; j < N + 2; j++)
{
B[i, j] = A[i, j];
}
}
for (int i = 0; i < N + 2; i++)
{
B[N + 2, i] = CardinalSpline.Cardinal(degree + 2, a_border, a_border + (i - (degree + 2) + 1) * h, h);
B[N + 3, i] = CardinalSpline.Cardinal(degree + 2, b_border, a_border + (i - (degree + 2) + 1) * h, h);
B[i, N + 2] = -B[N + 2, i];
B[i, N + 3] = -B[N + 3, i];
}
// Console.WriteLine(B);
//Console.WriteLine("b = " + b);
Vector c = Solver.BCG(B, b, 0.00000001d);
Console.WriteLine("anser = " + c);
Console.WriteLine("Ax = " + B * c);
Vector d = c.SubVector(0, N + 2);
CardinalSpline spline = new CardinalSpline();
Vector anser = spline.GetVectorFunction(10, a_border, b_border, d, h, degree + 2);
Vector expect = MyMath.Basic.GetVectorFunction(10, a_border, b_border, FunctionLib.cos);
Console.WriteLine(anser); Console.WriteLine(expect);
Console.WriteLine("||u - u_spl|| = " + (expect - anser).Norm);
}