使用四阶龙格库塔方法求解三体问题(解十二元一阶常微分方程组)

问题简化为三个质点的质量相同的情况

输入所求微分方程组的初值 t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3

输入所求微分方程组的微分区间[a,b]

输入所求微分方程组所分解子区间的个数step

输出文件可以直接用Matlab来作图

当时怎么写的我已经完全忘记了,我只记得当时很佩服自己

使用四阶龙格库塔方法求解三体问题(解十二元一阶常微分方程组)_第1张图片

以上是推导过程,然后给出代码实现:

  1 #include
  2 #include
  3 #include
  4 #include
  5 const double G=1;  //万有引力常量 
  6 double m;  //三个质点的同一质量 
  7 double initial[20],result[20];  //迭代数组 
  8 double a,b,h;  //区间和步长 
  9 double step;  //分段数 
 10 using namespace std;
 11 
 12 //以下六个函数对应六个位移对时间求导的微分方程 
 13 double fx1(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 14 {
 15     double dx1;
 16     dx1=vx1;
 17     return dx1;
 18 }
 19 double gy1(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 20 {
 21     double dy1;
 22     dy1=vy1;
 23     return dy1;
 24 }
 25 double fx2(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 26 {
 27     double dx2;
 28     dx2=vx2;
 29     return dx2;
 30 }
 31 double gy2(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 32 {
 33     double dy2;
 34     dy2=vy2;
 35     return dy2;
 36 }
 37 double fx3(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 38 {
 39     double dx3;
 40     dx3=vx3;
 41     return dx3;
 42 }
 43 double gy3(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 44 {
 45     double dy3;
 46     dy3=vy3;
 47     return dy3;
 48 }
 49 
 50 //以下六个函数对应速度对时间求导的微分方程 
 51 double fvx1(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 52 {
 53     double dvx1;
 54     dvx1=G*m*pow((y2-y1)*(y2-y1)+(x2-x1)*(x2-x1),-1.5)*(x2-x1)+G*m*pow((y3-y1)*(y3-y1)+(x3-x1)*(x3-x1),-1.5)*(x3-x1);
 55     return dvx1;
 56 }
 57 double gvy1(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 58 {
 59     double dvy1;
 60     dvy1=G*m*pow((y2-y1)*(y2-y1)+(x2-x1)*(x2-x1),-1.5)*(y2-y1)+G*m*pow((y3-y1)*(y3-y1)+(x3-x1)*(x3-x1),-1.5)*(y3-y1);
 61     return dvy1;
 62 }
 63 double fvx2(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 64 {
 65     double dvx2;
 66     dvx2=G*m*pow((y1-y2)*(y1-y2)+(x1-x2)*(x1-x2),-1.5)*(x1-x2)+G*m*pow((y3-y2)*(y3-y2)+(x3-x2)*(x3-x2),-1.5)*(x3-x2);
 67     return dvx2;
 68 }
 69 double gvy2(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 70 {
 71     double dvy2;
 72     dvy2=G*m*pow((y1-y2)*(y1-y2)+(x1-x2)*(x1-x2),-1.5)*(y1-y2)+G*m*pow((y3-y2)*(y3-y2)+(x3-x2)*(x3-x2),-1.5)*(y3-y2);
 73     return dvy2;
 74 }
 75 double fvx3(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 76 {
 77     double dvx3;
 78     dvx3=G*m*pow((y2-y3)*(y2-y3)+(x2-x3)*(x2-x3),-1.5)*(x2-x3)+G*m*pow((y1-y3)*(y1-y3)+(x1-x3)*(x1-x3),-1.5)*(x1-x3);
 79     return dvx3;
 80 }
 81 double gvy3(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
 82 {
 83     double dvy3;
 84     dvy3=G*m*pow((y2-y3)*(y2-y3)+(x2-x3)*(x2-x3),-1.5)*(y2-y3)+G*m*pow((y1-y3)*(y1-y3)+(x1-x3)*(x1-x3),-1.5)*(y1-y3);
 85     return dvy3;
 86 }
 87 //龙格库塔方法 
 88 void RK4(
 89          double (*fx1)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 90          double (*gy1)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 91          double (*fx2)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 92          double (*gy2)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 93          double (*fx3)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 94          double (*gy3)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 95          
 96          double (*fvx1)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 97          double (*gvy1)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 98          double (*fvx2)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
 99          double (*gvy2)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
100          double (*fvx3)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3),
101          double (*gvy3)(double t,double x1,double y1,double x2,double y2,double x3,double y3,double vx1,double vy1,double vx2,double vy2,double vx3,double vy3)
102         )
103 {
104     //前六个方程的中间值 
105     double x1f1,x1f2,x1f3,x1f4,y1g1,y1g2,y1g3,y1g4;
106     double x2f1,x2f2,x2f3,x2f4,y2g1,y2g2,y2g3,y2g4;
107     double x3f1,x3f2,x3f3,x3f4,y3g1,y3g2,y3g3,y3g4;
108     //后六个方程的中间值 
109     double vx1f1,vx1f2,vx1f3,vx1f4,vy1g1,vy1g2,vy1g3,vy1g4;
110     double vx2f1,vx2f2,vx2f3,vx2f4,vy2g1,vy2g2,vy2g3,vy2g4;
111     double vx3f1,vx3f2,vx3f3,vx3f4,vy3g1,vy3g2,vy3g3,vy3g4;
112     //迭代值 
113     double t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3;
114     double nx1,ny1,nx2,ny2,nx3,ny3,nvx1,nvy1,nvx2,nvy2,nvx3,nvy3;
115     //初始化 
116     t0=initial[0];
117     x1=initial[1];
118     y1=initial[2];
119     x2=initial[3];
120     y2=initial[4];
121     x3=initial[5];
122     y3=initial[6];
123     vx1=initial[7];
124     vy1=initial[8];
125     vx2=initial[9];
126     vy2=initial[10];
127     vx3=initial[11];
128     vy3=initial[12];
129     //计算k1 
130     x1f1=fx1(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
131     y1g1=gy1(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
132     x2f1=fx2(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
133     y2g1=gy2(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
134     x3f1=fx3(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
135     y3g1=gy3(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
136     
137     vx1f1=fvx1(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
138     vy1g1=gvy1(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
139     vx2f1=fvx2(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
140     vy2g1=gvy2(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
141     vx3f1=fvx3(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
142     vy3g1=gvy3(t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3);
143     //计算k2 
144     x1f2=fx1(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
145     y1g2=gy1(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
146     x2f2=fx2(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
147     y2g2=gy2(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
148     x3f2=fx3(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
149     y3g2=gy3(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
150     
151     vx1f2=fvx1(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
152     vy1g2=gvy1(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
153     vx2f2=fvx2(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
154     vy2g2=gvy2(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
155     vx3f2=fvx3(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
156     vy3g2=gvy3(t0+h/2,x1+h*x1f1/2,y1+h*y1g1/2,x2+h*x2f1/2,y2+h*y2g1/2,x3+h*x3f1/2,y3+h*y3g1/2,vx1+h*vx1f1/2,vy1+h*vy1g1/2,vx2+h*vx2f1/2,vy2+h*vy2g1/2,vx3+h*vx3f1/2,vy3+h*vy3g1/2);
157     //计算k3 
158     x1f3=fx1(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
159     y1g3=gy1(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
160     x2f3=fx2(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
161     y2g3=gy2(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
162     x3f3=fx3(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
163     y3g3=gy3(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
164     
165     vx1f3=fvx1(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
166     vy1g3=gvy1(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
167     vx2f3=fvx2(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
168     vy2g3=gvy2(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
169     vx3f3=fvx3(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
170     vy3g3=gvy3(t0+h/2,x1+h*x1f2/2,y1+h*y1g2/2,x2+h*x2f2/2,y2+h*y2g2/2,x3+h*x3f2/2,y3+h*y3g2/2,vx1+h*vx1f2/2,vy1+h*vy1g2/2,vx2+h*vx2f2/2,vy2+h*vy2g2/2,vx3+h*vx3f2/2,vy3+h*vy3g2/2);
171     //计算k4 
172     x1f4=fx1(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
173     y1g4=gy1(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
174     x2f4=fx2(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
175     y2g4=gy2(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
176     x3f4=fx3(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
177     y3g4=gy3(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
178     
179     vx1f4=fvx1(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
180     vy1g4=gvy1(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
181     vx2f4=fvx2(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
182     vy2g4=gvy2(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
183     vx3f4=fvx3(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
184     vy3g4=gvy3(t0+h,x1+h*x1f3,y1+h*y1g3,x2+h*x2f3,y2+h*y2g3,x3+h*x3f3,y3+h*y3g3,vx1+h*vx1f3,vy1+h*vy1g3,vx2+h*vx2f3,vy2+h*vy2g3,vx3+h*vx3f3,vy3+h*vy3g3);
185     //计算最终结果 
186     nx1=x1+h*(x1f1+2*x1f2+2*x1f3+x1f4)/6;
187     ny1=y1+h*(y1g1+2*y1g2+2*y1g3+y1g4)/6;
188     nx2=x2+h*(x2f1+2*x2f2+2*x2f3+x2f4)/6;
189     ny2=y2+h*(y2g1+2*y2g2+2*y2g3+y2g4)/6;
190     nx3=x3+h*(x3f1+2*x3f2+2*x3f3+x3f4)/6;
191     ny3=y3+h*(y3g1+2*y3g2+2*y3g3+y3g4)/6;
192     
193     nvx1=vx1+h*(vx1f1+2*vx1f2+2*vx1f3+vx1f4)/6;
194     nvy1=vy1+h*(vy1g1+2*vy1g2+2*vy1g3+vy1g4)/6;
195     nvx2=vx2+h*(vx2f1+2*vx2f2+2*vx2f3+vx2f4)/6;
196     nvy2=vy2+h*(vy2g1+2*vy2g2+2*vy2g3+vy2g4)/6;
197     nvx3=vx3+h*(vx3f1+2*vx3f2+2*vx3f3+vx3f4)/6;
198     nvy3=vy3+h*(vy3g1+2*vy3g2+2*vy3g3+vy3g4)/6;
199     //迭代过程 
200     result[0]=t0+h;
201     result[1]=nx1;
202     result[2]=ny1;
203     result[3]=nx2;
204     result[4]=ny2;
205     result[5]=nx3;
206     result[6]=ny3;
207     result[7]=nvx1;
208     result[8]=nvy1;
209     result[9]=nvx2;
210     result[10]=nvy2;
211     result[11]=nvx3;
212     result[12]=nvy3;
213 }
214 int main()
215 {
216     freopen("input.txt","r",stdin);
217     freopen("ouput.txt","w",stdout);
218     //cout<<"输入三个质点的相同质量m:"<219     //cin>>m;
220     m=1;
221     //cout<<"输入所求微分方程组的初值 t0,x1,y1,x2,y2,x3,y3,vx1,vy1,vx2,vy2,vx3,vy3:"<
222     initial[0]=0;
223     initial[1]=-1;
224     initial[2]=0;
225     initial[3]=1;
226     initial[4]=0;
227     initial[5]=0;
228     initial[6]=0;
229     cin>>initial[7]>>initial[8];
230     initial[9]=initial[7];
231     initial[10]=initial[8];
232     initial[11]=-2*initial[9];
233     initial[12]=-2*initial[10];
234     //cout<<"输入所求微分方程组的微分区间[a,b]:"<
235     cin>>a>>b;
236     
237     //cout<<"输入所求微分方程组所分解子区间的个数step:"<
238     cin>>step;
239     
240     cout<fixed)<10);
241     cout<15)<<"t"<15)<<"x1"<15)<<"y1"<15)<<"x2"<15)<<"y2"<15)<<"x3"<15)<<"y3";
242     cout<15)<<"Vx1"<15)<<"Vx2"<15)<<"Vy1"<15)<<"Vy2"<15)<<"Vx3"<15)<<"Vy3"<<endl;
243     h=(b-a)/step;  //计算步长 
244     for(int i=0;i<=12;i++)
245         cout<15)<//输出初始值 
246     cout<<endl;
247     for(int i=0;i)
248     {
249         RK4(fx1,gy1,fx2,gy2,fx3,gy3,fvx1,gvy1,fvx2,gvy2,fvx3,gvy3);
250         for(int i=0;i<=12;i++)
251             cout<15)<//输出每一次的迭代结果 
252         cout<<endl;
253         
254         for(int i=0;i<=12;i++)
255             initial[i]=result[i];  //迭代 
256     } 
257     return 0;
258 }

数值计算算是一个比较有意思的方向

转载于:https://www.cnblogs.com/aininot260/p/10039364.html

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