1. Solving the differential equation by Using the Runge-Kutta's
Method of order 4
Soongsin Joo
안녕하십니까?
저는 빛의 간섭과 회절 실험발표를 맡은 06학번 주숭신입니다.

2. Runge-Kutta's Method of order 4

3. Runge-Kutta's Method of order 4
dx/dt=f(x,t)라는 미분방정식이 t=t0 일때의 x값이 x0인 initial value를 갖을 때,
4차 Runge-Kutta’s Method로 상태변수 x(t)를 구하는 것이 문제이다.
Step Size 를 h라고 했을때,

4. Algorithm
Runge-Kutta’s method of order 4 to solve a first-order differential
equation

5. Runge-Kutta's Method of order 4 Source
/* Runge-Kutta's method of order 2 to solve a first-order differential equation */
/* Solve the system of single harmonic oscillator */
/* Include header files */
#include <stdio.h>
#include <math.h>
#include <conio.h>
#include <stdlib.h>
/* Define constant*/
#define w 2
#define h 0.01
/* Define global variables */
float t,x,v,SN,PT;
char FOUTN[20];
FILE *FOUT;
/* approximate solution state variable */
void RK4();
if((FOUT=fopen(FOUTN,"w"))==NULL){
printf("FILE OPEN ERROR...\n");
getch();
exit(-1); }
printf("INPUT THE NUMBER
OF STEPS PER ONE SECOND\n");
scanf("%f",&SN);
printf("INPUT PLOTTING TIME\n");
scanf("%f",&PN);
m=100; k=400; w=sqrt(k/m); h=1/SN;
t=0; x0=10; v0=0;
x=x0;v=v0;
for(i=0;i<=SN*PN;i++){
printf("%10.3E\t%10.3E\t%10.3E\n",t,x,v);
fprintf(FOUT,"%10.3E\t
%10.3E\t%10.3E\n",t,x,v);
RKM4();
fclose(FOUT);

6. Runge-Kutta's Method of order 4 Source
void RK4(){
float ti,xi,vi,f1,f2,f3,f4,g1,g2,g3,g4; /* Define local variable */
ti=t; xi=x; vi=v;
f1=F(v); g1=G(x);
x=xi+h*f1/2; v=vi+h*g1/2;
t=ti+h/2;
f2=F(v); g2=G(x);
x=xi+h*f2/2; v=vi+h*g2/2;
f3=F(v); g3=G(x);
t=ti+h;
x=xi+h*f3; v=vi+h*g3;
f4=F(v); g4=G(x);
x=xi+h*(f1+2*f2+2*f3+f4)/6;
v=vi+h*(g1+2*g2+2*g3+g4)/6; }
/* dx/dt=F(x(t),v(t),t)=v */
float F(float V){
float f;
f=V;
return f; }
/* dv/dt=G(x(t),v(t),t)=-w*w*x */
float G(float X){
float g;
g=-w*w*X;
return g;