int main () {
int N, M = 10;
N = 10;
double h, Cx = 1.0, k = 0.6;
h = 2.0/N; //Piece size
double tau;
tau = k*h/Cx;
int i;
double x[11];
for (i = 0; i < (N+1); i++) {
x[i] =i*h - 1;
}
double U[11];
for (i = 0; i < (N+1); i++) {
U[i] = 0;
if ((x[i]>=(-0.5))&&(x[i]<=0.5)) {
U[i] = 1;
}
}
double a;
for (i = 0; M > 0; i++) {
if (i == 0) {
a = (U[i] - U[N])/(x[i]-x[N]);
} else {
a = (U[i] - U[i-1])/(x[i]-x[i-1]);
}
// y=ax+b; U[i-1]
U[i]=(x[i] - Cx*tau)*a + U[i-1]-a*x[i-1];
DM_plot_1d(x, U, N, "Test 1", 1);
M--;
printf("%f ", U[i]);
if (i == N) {
//M--;
i = 0;
//DM_plot_1d(x, U, N, "Test 1", 1);
//DM_plot_1d(x, U, N, "Test 1", 0);
printf("\n");
}
}
return 0;
}
int main(){
const double Cx = 1;
const double k = 0.5;
int N, M;
double x[100] = {0};
double y[100] = {0};
double previous_y[100] = {0};
double previous_der[100] = {0};
double der[100] = {0};
double h, t;
scanf("%d", &N);
h = 2.0 / N;
t = (k * h) / Cx;
M = 2.0 / (Cx * t)+1; // amount of steps
int i;
for (i = 0; i < N; i++) {
x[i] = (i * h) - 1;
y[i] = previous_y[i] = init (x[i]);
};
double A, B, C, D, tg, b;
int j = 0;
while (j < M) {
for (i = 1; i < N; i++) {
D = y[i];
C = der[i];
A = (((previous_der[i-1] - C)/h) + 2 * (previous_y[i-1] - D + C * h)/(h*h))/h;
B = (previous_y[i-1] - D + C * h)/(h*h) + A*h;
y[i] = A * (-Cx*t) * (-Cx*t) * (-Cx*t) + B * (-Cx*t) * (-Cx*t) + C * (-Cx*t) + D;
der[i] = 3 * A * (-Cx*t) * (-Cx*t) + 2 * B * (-Cx*t) + C;
};
D = y[0];
C = der[0];
A = (((previous_der[N - 1] - C)/h) + 2 * (previous_y[N-1] - D + C * h)/(h*h))/h;
B = (previous_y[N-1] - D + C * h)/(h*h) + A*h;
y[0] = A * (-Cx*t) * (-Cx*t) * (-Cx*t) + B * (-Cx*t) * (-Cx*t) + C * (-Cx*t) + D;
der[0] = 3 * A * (-Cx*t) * (-Cx*t) + 2 * B * (-Cx*t) + C;
for (i = 0; i < N; i++){
previous_y[i] = y[i];
previous_der[i] = der[i];
}
j++;
}
//build plot
DM_plot_1d(x, y, N, "Test 1", 0);
DM_plot_1d(x, y, N, "Test 1", 1);
return 0;
}
int main()
{
int i;
int N = 100;//N is the number of nodes
double cx = 1.0;
double k = 0.6;
double *current = (double *)malloc(N*sizeof(double));
double *next = (double *)malloc(N*sizeof(double));
double *current_der = (double *)malloc(N*sizeof(double));
double *next_der = (double *)malloc(N*sizeof(double));
double *x = (double *)malloc(N*sizeof(double));
//initialization
double tau, h;
h = 2.0/N;
tau = k*h/cx;
float eps = 0.0000001;
for (i = 0; i < N; i++)
{
if ( ((-1.0 + i*h) >= -0.5 ) && ((-1.0 + i*h) <= 0.5 ) )
current[i] = 1.0;
else
current[i] = 0.0;
next[i] = 0.0;
current_der[i] = 0.0;
next_der[i] = 0.0;
x[i] = -1.0 + i*h;
}
DM_plot_1d(x, current, N, "Text", 1);
// print(N, current);
//main loop
int j;
double a, b, c, d, A, B, C, D, E, F, x0;
double xm, xm_1, um, um_1, dum, dum_1;
//here um stands for a u(xm), dum for derivative of u in xm
//extrapolation as a polinom ax^3+bx^2+cx+d
i = 0;
while (i < 2/(cx*tau)) //1 period {
for (j = 0; j < N-1; j++)
{
//description of new values
um = current[j+1];
um_1 = current[j];
dum = current_der[j+1];
dum_1 = current_der[j];
xm_1 = -1.0 + j*h;
xm = -1.0 + (j+1)*h;
x0 = xm - cx*tau;
if ( (fabs(xm-0.0) > eps) && (fabs(xm_1-0.0) > eps) )
{
//calculation of coefficients
A = -0.5*(xm_1*xm_1*xm_1 - xm*xm*xm);
B = 0.5*(xm_1 - xm);
C = um_1 - um +0.5*(xm*dum - xm_1*dum_1);
D = -3.0*xm_1*xm*(xm - xm_1);
E = xm - xm_1;
F = dum_1*xm - dum*xm_1;
a = (C*E - F*B)/(A*E - D*B);
c = (A*F - D*C)/(A*E - D*B);
b = (dum - 3.0*a*xm*xm - c)/(2.0*xm);
d = um - c*xm - b*xm*xm - a*xm*xm*xm;
}
if (fabs(xm_1-0.0) < eps)
{
d = um_1;
c = dum_1;
A = um-c*xm-d;
B = dum-c;
a = -(A*2.0-B*xm)/(xm*xm*xm);
b = -(xm*B-3.0*A)/(xm*xm);
}
if (fabs(xm-0.0) < eps)
{
d = um;
c = dum;
A = um_1-c*xm_1-d;
B = dum_1-c;
a = -(A*2.0-B*xm_1)/(xm_1*xm_1*xm_1);
b = -(xm_1*B-3.0*A)/(xm_1*xm_1);
}
//recalculation of function and its derivative
next[j+1] = a*x0*x0*x0 + b*x0*x0 + c*x0 + d;
next_der[j+1] = 3.0*a*x0*x0 + 2.0*b*x0 + c;
}
//the same for the border layer
um = current[0];
um_1 = current[N-1];
dum = current_der[0];
dum_1 = current_der[N-1];
xm_1 = -1.0 + (N-1)*h;
xm = -1.0 + N*h;
x0 = xm - cx*tau;
A = -0.5*(xm_1*xm_1*xm_1 - xm*xm*xm);
B = 0.5*(xm_1 - xm);
C = um_1 - um +0.5*(xm*dum - xm_1*dum_1);
D = -3.0*xm_1*xm*(xm - xm_1);
E = xm - xm_1;
F = dum_1*xm - dum*xm_1;
a = (C*E - F*B)/(A*E - D*B);
c = (A*F - D*C)/(A*E - D*B);
b = (dum - 3.0*a*xm*xm - c)/(2.0*xm);
d = um - c*xm - b*xm*xm - a*xm*xm*xm;
next[0] = a*x0*x0*x0 + b*x0*x0 + c*x0 + d;
next_der[0] = 3.0*a*x0*x0 + 2.0*b*x0 + c;
//current arrays update
for (j = 0; j < N; j++)
{
current[j] = next[j];
current_der[j] = next_der[j];
}
DM_plot_1d(x, current, N, "Text", 1);
i++;
}
