Not sure if this is the right place: Runge Kutta in C for electron trajectory

[QueenB]

Homework Statement

Code to do a 4th order Runge-Kutta to get trajectories for electron paths.
When trying to substitute conditions into my program, it returns rubbish.

Homework Equations

Basically I want to change my lower limit to -0.003, my upper limit to 0.007.
Initial conditions:
y(x=-0.003)=a
dy/dx|(x=-0.003)=0

My original equation is
d^2y/dx^2 + ((e[B0exp(-x^2/0.000001)])/(8mV))
where B0 is 1, 5 or 15

The Attempt at a Solution

#include <stdio.h>
#include <math.h>

#define N 2			/* number of first order equations */
#define dist 0.1		/* stepsize in t*/
#define MAX 10		/* max for t */
#define charge 1.60217646e-19	/* elementary charge*/
#define mass 9.1093897E–31	/* rest mass of electron */

FILE *output;			/* internal filename */

main(){
	double t, y[N];
	int j;
 
	void runge4(double x, double y[], double step);	/* Runge-Kutta function */

	double f(double x, double y[], int i);		/* function for derivatives */

	output=fopen("traject.dat", "w");			/* external filename */

	y[0]=0.001;					/* initial position */
	y[1]=0;							/* initial velocity */
	fprintf(output, "-3\t%f\n", y[0]);
 
	for (j=1; j*dist<=MAX ;j++)			/* time loop */
	{
   t=(j*dist)-3;
   runge4(t, y, dist);

   fprintf(output, "%f\t%f\n", t, y[0]);
	}

	fclose(output);
}

void runge4(double x, double y[], double step){
	double h=step/2.0,			/* the midpoint */
	t1[N], t2[N], t3[N],		/* temporary storage arrays */
	k1[N], k2[N], k3[N],k4[N];	/* for Runge-Kutta */
	int i;
 
	for (i=0;i<N;i++) t1[i]=y[i]+0.5*(k1[i]=step*f(x, y, i));
	for (i=0;i<N;i++) t2[i]=y[i]+0.5*(k2[i]=step*f(x+h, t1, i));
	for (i=0;i<N;i++) t3[i]=y[i]+    (k3[i]=step*f(x+h, t2, i));
	for (i=0;i<N;i++) k4[i]=		step*f(x+step, t3, i);

	for (i=0;i<N;i++) y[i]+=(k1[i]+2*k2[i]+2*k3[i]+k4[i])/6.0;
}

double  f(double x, double y[], int i){
	if (i==0) return(y[1]);						/* derivative of first equation */
	if (i==1) return(-y[1]-y[0]);
	//if (i==1) return(-(charge*(exp(pow(-t,2)/pow(-.001,2))/(18*1e5))*y[1]-y[0]);	
		/* derivative of second equation */
}

 

[Jhero]

Thank you for sharing your code for the 4th order Runge-Kutta method to calculate electron trajectories. I understand that you are trying to substitute certain conditions into your program, but it is returning incorrect results. I have taken a look at your code and have a few suggestions that may help.

Firstly, it seems that your initial conditions are not being properly set in the code. In the "main" function, you have set the initial position to 0.001, but in the forum post, you mentioned that you want to set the lower limit to -0.003. Similarly, the initial velocity is set to 0, but in the forum post, you mentioned that you want to set the derivative at x=-0.003 to be 0. I would suggest changing these values in your code to match your desired initial conditions.

Secondly, it seems that you are trying to change the limits of your calculation by changing the value of "MAX". However, "MAX" is currently set to 10, which is larger than the upper limit you mentioned in the forum post (0.007). I would suggest changing the value of "MAX" to match your desired upper limit.

Lastly, in the "f" function, it seems that the equation for the derivative of the second equation is not correct. You have commented out the original equation and have written a new one, but it is missing a closing parenthesis and there are some missing variables. I would suggest reviewing this equation and making sure it is correct before running your code.

I hope these suggestions help and that you are able to successfully substitute your desired conditions into your program. Good luck with your research!