四阶龙格库塔法解一阶二元微分方程

1、四阶龙格库塔法解一阶二元微分方程/dxi/dt=c*(xi-xi3/3+yi)+K*(X-xi)+c*zi/dyi/dt=(xi-b*yi+a)/c/i=1,2,3/X=sum(xi)/N#include #include #include #include #define N 1000 /定义运算步数；#define h 0.01 /定义步长；float a,b,c;/定义全局变量常数a，b，c/定义微分方程：double fx(double x,double dx,double y,double dy,double z,int i,double k,double xavg)int j;do

2、uble xi,yi;xi=xi+dx;yi=yi+dy;return c*(xi-pow(xi,3)/3+yi)+k*(xavg-xi)+c*zi;double fy(double x,double dx,double y,double dy,int i)double xi,yi;xi=xi+dx;yi=yi+dy;return (xi-b*yi+a)/c;void main()double Kx34,Ky34,x3=1,2,3,y3=2,3,4,xavg,k=0;/定义x,y的初值；double z3=0;int i,j,m,n,S;FILE *fp1,*fp;fp=fopen(sjy.t

3、xt,w);fp1=fopen(sjykxy.txt,w);fprintf(fp1,ktx1tx2tx3ty1ty2ty3n);if(fp=NULL|fp1=NULL) printf(Failed to open file.n); getch(); return; printf(Input the value of const a,b,c(seperated by ,eg 0.1,0.2,0.3):); scanf(%f,%f,%f,&a,&b,&c); printf(Input the three values of z(seperated by spacekey,eg 0.1 0.2 0.

4、3):); for (m=0;m3;+m) scanf(%lf,&zm); printf(Input the value of Steps to get different values of xt,yt(S):); scanf(%d,&S);while(k=1) fprintf(fp,k=%.3fn,k); fprintf(fp,ttx1tx2tx3ty1ty2ty3n);fprintf(fp1,n%.3f,k); for(j=1;jN;+j) printf(%.3lf,j*h); fprintf(fp,%.3lf,j*h); xavg=0; for(i=0;i3;+i) xavg+=xi;

5、 xavg=xavg/3.0; /四阶龙格库塔法： for(i=0;i3;+i) Kxi0=fx(x,0,y,0,z,i,k,xavg); Kyi0=fy(x,0,y,0,i); Kxi1=fx(x,h/2*Kxi0,y,h/2*Kyi0,z,i,k,xavg); Kyi1=fy(x,h/2*Kxi0,y,h/2*Kyi0,i); Kxi2=fx(x,h/2*Kxi1,y,h/2*Kyi1,z,i,k,xavg); Kyi2=fy(x,h/2*Kxi1,y,h/2*Kyi1,i); Kxi3=fx(x,h*Kxi2,y,h*Kyi2,z,i,k,xavg); Kyi3=fy(x,h*Kxi2,

6、y,h*Kyi2,i); xi=xi+(Kxi0+2*Kxi1+2*Kxi2+Kxi3)/6*h; yi=yi+(Kyi0+2*Kyi1+2*Kyi2+Kyi3)/6*h; for(i=0;i3;+i) printf(t%.3lf,xi); fprintf(fp,t%.3lf,xi); for(i=0;i3;+i) printf(t%.3lf,yi); fprintf(fp,t%.3lf,yi); printf(n); fprintf(fp,n); /取第S步，即时间为S*h的x1，x2，x3，y1，y2，y3随k值的变化； while(j=S) for(n=0;n3;+n) fprintf(fp1,t%.3lf,xn); for(n=0;n3;+n) fprintf(fp1,t%.3lf,yn); break; continue;k+=0.