//u'' = f; u(a) = u0 u(b) = u1
public static void SolveSecondDerevetivWhithBounderyCondition(int SIZE, double a_border, double b_border,
ICardinalStratagy calculate,
double u0, double u1, FunctionLib.Function function)
{
int degree = 4;
int N = SIZE;
int M = N + degree - 2;
int m = degree - 2;
Matrix U = new Matrix(m, M);
double h = MyMath.Basic.GetStep(N, a_border, b_border);
CardinalSpline spline = new CardinalSpline(calculate);
Matrix D = (1d / Math.Pow(h, m)) * CardinalOperators.DerevetiveMatrix(degree, SIZE);
//условие 1: (c,ksi(a)) = u0
Vector ksi_a = spline.SplineVector(a_border, a_border, b_border, N, degree);
//условие 1: (c,ksi(b)) = u1
Vector ksi_b = spline.SplineVector(b_border, a_border, b_border, N, degree);
for (int i = 0; i < M; i++)
{
U[0, i] = ksi_a[i];
U[1, i] = ksi_b[i];
}
//-------------
//Составляем линейную систему
Matrix A = ConstructMatrix(D, U);
//Составляем правую часть
Vector b = MyMath.Basic.GetVectorFunction(N, a_border, b_border, function);
Vector y = Matrix.Transpose(D) * b;
Vector y_prime = new Vector(y.Length + m);
y_prime[y.Length] = u0;
y_prime[y.Length + 1] = u1;
for (int i = 0; i < y.Length; i++)
{
y_prime[i] = y[i];
}
Console.WriteLine("right part = " + y_prime);
// Console.WriteLine(A);
Vector x = Solver.BCG(A, y_prime, 0.0001d);
Console.WriteLine("x = " + x);
Vector c = x.SubVector(0, M);
Vector f = spline.GetVectorFunction(N, a_border, b_border, c, h, degree);
Console.WriteLine("f = " + f);
f = spline.GetVectorFunction(10 * N, a_border, b_border, c, h, degree);
b = MyMath.Basic.GetVectorFunction(10 * N, a_border, b_border, function);
Console.WriteLine("||err|| = " + (f - b).Norm);
}
public static Matrix D1_Matrix(int SIZE, double a_border, double b_border,
ICardinalStratagy calculate)
{
int degree = 3;
int N = SIZE;
int M = N + degree - 2;
int m = degree - 2;
Matrix U = new Matrix(m, M);
double h = MyMath.Basic.GetStep(N, a_border, b_border);
CardinalSpline spline = new CardinalSpline(calculate);
Matrix D = (1d / h) * CardinalOperators.DerevetiveMatrix(degree, SIZE);
//условие 1: (c,ksi(a)) = u0
Vector ksi_a = spline.SplineVector(a_border, a_border, b_border, N, degree);
for (int i = 0; i < M; i++)
{
U[0, i] = ksi_a[i];
}
//-------------
//Составляем линейную систему
Matrix A = ConstructMatrix(D, U);
return(A);
}
public static Matrix D4_B_Matrix(int SIZE, double a_border, double b_border,
ICardinalStratagy calculate)
{
int degree = 6;
int N = SIZE;
int M = N + degree - 2;
int m = degree - 2;
double alpha = 0.5d;
Matrix U = new Matrix(m, M);
double h = MyMath.Basic.GetStep(N, a_border, b_border);
double h4 = Math.Pow(h, 4);
CardinalSpline spline = new CardinalSpline(calculate);
Matrix D = (1d / h4) * CardinalOperators.DerevetiveMatrix(degree, SIZE) +
(-Math.Pow(alpha, 1)) * CardinalOperators.InterpolateConditionMatrix(degree, SIZE, calculate);
//условие 1: (c,ksi(a)) = u0
Vector ksi_a = spline.SplineVector(a_border, a_border, b_border, N, degree);
//условие 1: (c,ksi(b)) = u1
Vector ksi_b = spline.SplineVector(b_border, a_border, b_border, N, degree);
//условие 2: (c,TD2*ksi(a,deg - 2)) = du0
Matrix D2 = Matrix.Transpose(((1d / Math.Pow(h, 2)) * CardinalOperators.DerevetiveMatrix(4, SIZE + 2)));
Vector Dksi_a = D2 * spline.SplineVector(a_border, a_border, b_border, N, degree - 2);
//условие 2: (c,TD2*ksi(a,deg - 2)) = du1
Vector Dksi_b = D2 * spline.SplineVector(b_border, a_border, b_border, N, degree - 2);
for (int i = 0; i < M; i++)
{
U[0, i] = ksi_a[i];
U[1, i] = ksi_b[i];
U[2, i] = Dksi_a[i];
U[3, i] = Dksi_b[i];
}
//-------------
//Составляем линейную систему
Matrix A = ConstructMatrix(D, U);
return(A);
}
//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 static Matrix InterpolateConditionMatrix(int degree, int SIZE, ICardinalStratagy calculate)
{
int N = SIZE;
int M = N + degree - 2;
uint p = (uint)(degree - 2);
Matrix D = new Matrix(N, M);
double[] val = calculate.GetCardinalValue(degree);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < val.Length; j++)
{
D[i, i + j] = val[j];
}
}
return(D);
}
//u'''' - alpha*u = f; u(a) = u0 u(b) = u1; u(a) = du0 u(b) = du1
public static void D4_B_bc(int SIZE, double a_border, double b_border,
ICardinalStratagy calculate,
double u0, double u1, double du0, double du1,
FunctionLib.Function function)
{
int degree = 6;
int N = SIZE;
int M = N + degree - 2;
int m = degree - 2;
double alpha = 0.5d;
Matrix U = new Matrix(m, M);
double h = MyMath.Basic.GetStep(N, a_border, b_border);
double h4 = Math.Pow(h, 4);
CardinalSpline spline = new CardinalSpline(calculate);
Matrix D = (1d / h4) * CardinalOperators.DerevetiveMatrix(degree, SIZE) +
(-Math.Pow(alpha, 1)) * CardinalOperators.InterpolateConditionMatrix(degree, SIZE, calculate);
//условие 1: (c,ksi(a)) = u0
Vector ksi_a = spline.SplineVector(a_border, a_border, b_border, N, degree);
//условие 1: (c,ksi(b)) = u1
Vector ksi_b = spline.SplineVector(b_border, a_border, b_border, N, degree);
//условие 2: (c,TD2*ksi(a,deg - 2)) = du0
Matrix D2 = Matrix.Transpose(((1d / Math.Pow(h, 2)) * CardinalOperators.DerevetiveMatrix(4, SIZE + 2)));
Vector Dksi_a = D2 * spline.SplineVector(a_border, a_border, b_border, N, degree - 2);
//условие 2: (c,TD2*ksi(a,deg - 2)) = du1
Vector Dksi_b = D2 * spline.SplineVector(b_border, a_border, b_border, N, degree - 2);
for (int i = 0; i < M; i++)
{
U[0, i] = ksi_a[i];
U[1, i] = ksi_b[i];
U[2, i] = Dksi_a[i];
U[3, i] = Dksi_b[i];
}
//-------------
//Составляем линейную систему
Matrix A = ConstructMatrix(D, U);
//Составляем правую часть
Vector b = MyMath.Basic.GetVectorFunction(N, a_border, b_border, function);
Vector y = Matrix.Transpose(D) * b;
Vector y_prime = new Vector(y.Length + m);
y_prime[y.Length] = u0;
y_prime[y.Length + 1] = u1;
y_prime[y.Length + 2] = du0;
y_prime[y.Length + 3] = du1;
for (int i = 0; i < y.Length; i++)
{
y_prime[i] = y[i];
}
Console.WriteLine("right part = " + y_prime);
//Console.WriteLine(A);
A.Save("D4.txt");
/*
* Vector x = Solver.BCG(A, y_prime, 0.0001d);
* Console.WriteLine("x = " + x);
* Vector c = x.SubVector(0, M);
* Vector f = spline.GetVectorFunction(N, a_border, b_border, c, h, degree);
* Console.WriteLine("f = " + f);
* f = spline.GetVectorFunction(10 * N, a_border, b_border, c, h, degree);
* b = MyMath.Basic.GetVectorFunction(10 * N, a_border, b_border, Math.Sin);
* Console.WriteLine("||err|| = " + (f - b).Norm);*/
}
public CardinalSpline(ICardinalStratagy strategy)
{
this.calculate = strategy;
}
public CardinalSpline()
{
calculate = new DividedDifferencesStategy();
}
