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Copy pathIntegrador2.c
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Integrador2.c
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#include <stdio.h>
#include <math.h>
void RK4_step(double delta_t, double e, double t, double *x, double *v,double *x3,double *v3);
void leapfrog_step(double delta_t,double e, double t, double *x, double *v,double *x3, double *v3);
double deriv_x(double t, double x, double v);
double deriv_v(double t, double x, double v,double e);
double deriv_v3(double t, double x3,double x, double v, double e);
FILE *file1;
FILE *file2;
int main(){
double x_RK4, x_LF, x3_RK4,x3_LF;
double v_RK4, v_LF, v3_RK4,v3_LF;
double t;
double x3_CI;
double T=2800;
double delta_t=6E-3;
int n_step = (int)(T/delta_t);
double x_step = 0.0, e=1;
double v_step = 0.0;
int i,j;
file1 = fopen("salida1LF.dat", "w");
file2 = fopen("salida1RK4.dat", "w");
t=0.0;
x_RK4=0.4325;
v_RK4=0.0;
x3_RK4=0.0;
v3_RK4=0.0;
x3_LF=0.0;
v_LF=0.0;
x_LF=0.4325;
v3_LF=0.0;
x3_CI=0.0;
for(j=0;j<1000;j++){
x3_LF=x3_CI;
v_LF=0.0;
x_LF=0.4325;
v3_LF=0.0;
x3_RK4=x3_CI;
v_RK4=0.0;
x_RK4=0.4325;
v3_RK4=0.0;
for(i=0;i<n_step;i++){
if(fabs(v_LF)<0.0005)
fprintf(file1,"%f %.15e %.15e %.15e %.15e \n", t, x_LF, v_LF, x3_LF, v3_LF);
if(fabs(v_RK4)<0.0005)
fprintf(file2,"%f %.15e %.15e %.15e %.15e \n", t, x_LF, v_LF, x3_RK4, v3_RK4);
RK4_step(delta_t,e, t, &x_RK4, &v_RK4, &x3_RK4, &v3_RK4);
leapfrog_step(delta_t,e, t, &x_LF, &v_LF,&x3_LF,&v3_LF);
t += delta_t;
}
x3_CI+=0.002;
}
fclose(file1);
fclose(file2);
return 0;
}
double deriv_x(double t, double x, double v){
return v;
}
double deriv_v(double t, double x, double v, double e){
return -2.0*x/pow(4*x*x+e,1.5);
}
double deriv_x3(double t, double x3, double v3){
return v3;
}
double deriv_v3(double t, double x3,double x, double v, double e){
return (x-x3)/pow(pow((x-x3),2)+pow(e,2)/4,1.5)-(x+x3)/pow(pow((x+x3),2)+pow(e,2)/4,1.5);
}
void leapfrog_step(double delta_t,double e, double t, double *x, double *v,double *x3,double *v3){
double x_in,x3_in;
double v_in,v3_in;
x_in = *x;
v_in = *v;
x3_in=*x3;
v3_in=*v3;
x_in += 1/(2*(2-pow(2,1/3)))* v_in * delta_t;
v_in += 1/(2-pow(2,1/3)) * deriv_v(t,x_in,v_in,e) * delta_t;
x_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v_in * delta_t;
v_in += -pow(2,1/3)/(2-pow(2,1/3)) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v_in * delta_t;
v_in += 1/(2-pow(2,1/3)) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += 1/(2*(2-pow(2,1/3))) * v_in * delta_t;
x3_in += 1/(2*(2-pow(2,1/3))) * v3_in * delta_t;
v3_in += 1/(2-pow(2,1/3)) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v3_in * delta_t;
v3_in += -pow(2,1/3)/(2-pow(2,1/3)) * deriv_v3(t, x3_in,x_in, v_in,e) * delta_t;
x3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v3_in * delta_t;
v3_in += 1/(2-pow(2,1/3)) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += 1/(2*(2-pow(2,1/3))) * v3_in * delta_t;
/*v_in += 1/(2*(2-pow(2,1/3)))* deriv_v(t,x_in,v_in,e) * delta_t;
x_in += 1/(2-pow(2,1/3)) * v_in * delta_t;
v_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += -pow(2,1/3)/(2-pow(2,1/3)) * v_in * delta_t;
v_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += 1/(2-pow(2,1/3)) * v_in * delta_t;
v_in += 1/(2*(2-pow(2,1/3)))* deriv_v(t, x_in, v_in,e) * delta_t;
v3_in += 1/(2*(2-pow(2,1/3))) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += 1/(2-pow(2,1/3)) * v3_in * delta_t;
v3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v3(t, x3_in,x_in, v_in,e) * delta_t;
x3_in += -pow(2,1/3)/(2-pow(2,1/3)) * v3_in * delta_t;
v3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += 1/(2-pow(2,1/3)) * v3_in * delta_t;
v3_in += 1/(2*(2-pow(2,1/3))) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;*/
*x = x_in;
*v = v_in;
*x3=x3_in;
*v3=v3_in;
}
void RK4_step(double delta_t, double e, double t, double *x, double *v,double *x3,double *v3){
double k1, k2, k3, k4;
double l1, l2, l3, l4;
double m1, m2, m3, m4;
double n1, n2, n3, n4;
double x_in;
double v_in;
double x3_in;
double v3_in;
x_in = *x;
v_in = *v;
x3_in = *x3;
v3_in = *v3;
k1 = deriv_x(t,x_in,v_in);
l1 = deriv_v(t,x_in,v_in,e);
k2 = deriv_x(t + delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5);
l2 = deriv_v(t + delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5,e) ;
k3 = deriv_x(t + delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5);
l3 = deriv_v(t + delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5,e);
k4 = deriv_x(t + delta_t, x_in + k3*delta_t, v_in + l3*delta_t);
l4 = deriv_v(t + delta_t, x_in + k3*delta_t, v_in + l3*delta_t,e);
x_in += (k1/6.0 + k2/3.0 + k3/3.0 + k4/6.0)*delta_t;
v_in += (l1/6.0 + l2/3.0 + l3/3.0 + l4/6.0)*delta_t;
m1 = deriv_x3(t,x3_in,v3_in);
n1 = deriv_v3(t,x3_in,x_in,v_in,e);
m2 = deriv_x3(t + delta_t*0.5, x3_in + m1*delta_t*0.5, v3_in + n1*delta_t*0.5);
n2 = deriv_v3(t + delta_t*0.5, x3_in + m1*delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5,e) ;
m3 = deriv_x3(t + delta_t*0.5, x3_in + m2*delta_t*0.5, v3_in + n2*delta_t*0.5);
n3 = deriv_v3(t + delta_t*0.5, x3_in + m2*delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5,e);
m4 = deriv_x3(t + delta_t, x3_in + m3*delta_t, v3_in + n3*delta_t);
n4 = deriv_v3(t + delta_t, x3_in + m3*delta_t, x_in + k3*delta_t, v_in + l3*delta_t,e);
x3_in += (m1/6.0 + m2/3.0 + m3/3.0 + m4/6.0)*delta_t;
v3_in += (n1/6.0 + n2/3.0 + n3/3.0 + n4/6.0)*delta_t;
*x = x_in;
*v = v_in;
*x3 = x3_in;
*v3 = v3_in;
}