//du/dt = d2u/d2s + f(t,s); du/dt = 0;
public static Vector SolveSliceTask1(Vector u_old, Vector f, Vector p, double nu, double h, double tau, double aa, int iter_t)
{
int n = u_old.Length;
Vector u_mid = new Vector(n);
Vector u_up = new Vector(n);
Vector u_down = new Vector(n);
Vector F = new Vector(n);
double left = -aa * tau / (h * h);
double right = -aa * tau / (h * h);
double middle = 1d + 2d * aa * tau / (h * h);
for (int i = 1; i < n - 1; i++)
{
F[i] = tau * f[i] + u_old[i];
u_mid[i] = middle;
u_up[i] = left;
u_down[i] = right;
}
u_down[0] = 0;
u_mid[0] = 1d + (h * h) / (aa * 2d * tau); //y[0]
u_up[0] = -1d; //y[1]
F[0] = (f[0] + u_old[0] / tau) * (h * h) / 2d * aa;
u_down[n - 1] = -1d; //y[N - 1]
u_mid[n - 1] = 1d + (h * h) / (aa * 2d * tau) + h * nu; //y[N]
u_up[n - 1] = 0;
double gamma_t = nu * p[iter_t];
F[n - 1] = (f[n - 1] + u_old[n - 1] / tau) * (h * h) / (2d * aa) + gamma_t * h;
Vector u = MyMath.TridiagonalMatrixAlgorithm(u_down, u_mid, u_up, F);
return(u);
}
// du/dt = -aa*d2u/d2s
public static Vector SolveSliceTask2(Vector u_old, double nu, double h, double tau, double aa)
{
int n = u_old.Length;
Vector u_mid = new Vector(n);
Vector u_up = new Vector(n);
Vector u_down = new Vector(n);
double left = -aa * tau / (h * h);
double right = -aa * tau / (h * h);
double middle = 1d + 2d * aa * tau / (h * h);
for (int i = 1; i < n - 1; i++)
{
u_mid[i] = middle;
u_up[i] = left;
u_down[i] = right;
}
u_down[0] = 0;
u_mid[0] = -(1d - h * h / (2d * aa * tau)); //y[0]
u_up[0] = 1d; // y[1]
u_old[0] = u_old[0] * (h * h / (2d * aa * tau));
u_down[n - 1] = 1d; //y[N-1]
u_mid[n - 1] = -1d - nu * h + (h * h) / (2d * aa * tau); //y[N]
u_up[n - 1] = 0;
u_old[n - 1] = u_old[n - 1] * (h * h) / (2d * aa * tau);
Vector u = MyMath.TridiagonalMatrixAlgorithm(u_down, u_mid, u_up, u_old);
return(u);
}
