龍格庫(kù)塔算法解微分方程組c語(yǔ)言

1、/*************************************************************************** This program is to solve the initial value problem of following system of differential equations: dx/dt=x+2*y,x(0)=0, dy/dt=2*x+y,y(0)=2, x(0

2、.2) and y(0.2) are to be calculated ****************************************************************************/ #include #include #define steplength 0.1 //步?長(zhǎng)¡è可¨¦根¨´據(jù)Y需¨¨要°

3、a調(diào)Ì¡Â整?; #define FuncNumber 2 //FuncNumber為a微¡é分¤?方¤?程¨¬的Ì?數(shù)ºy目?; void main() {float x[200],Yn[20][200],reachpoint;int i; x[0]=0;Yn[0][0]=0;Yn[1][0]=2; //初?值&

4、#166;Ì條¬?件t; reachpoint=0.2; //所¨´求¨®點(diǎn)Ì?可¨¦根¨´據(jù)Y需¨¨要°a調(diào)Ì¡Â整?; void rightfunctions(float x ,float *Auxiliary,float

5、*Func); void Runge_Kutta(float *x,float reachpoint, float(*Yn)[200]); Runge_Kutta(x ,reachpoint, Yn); printf(“x “); for(i=0;i<=(reachpoint-x[0])/steplength;i++)printf(“%f “,x[i]);printf(“\nY1 “); for(i=0;i<=(reach

6、point-x[0])/steplength;i++)printf(“%f “,Yn[0][i]);printf(“\nY2 “); for(i=0;i<=(reachpoint-x[0])/steplength;i++)printf(“%f “,Yn[1][i]);getchar();} void rightfunctions(float x ,float *Auxiliary,float *Func)//當(dāng)Ì

7、1;À右®¨°方¤?程¨¬改?變À? 時(shí)º¡À，ê?需¨¨要°a改?變À?; { Func[0]=Auxiliary[0]+2*Auxiliary[1]; Func[1]=2*Auxiliary[0]+Auxiliary[1];} void Runge_Kutta(float

8、 *x,float reachpoint, float(*Yn)[200]) {int i,j; float Func[FuncNumber],K[FuncNumber][4],Auxiliary[FuncNumber];for(i=0;i<=(reachpoint-x[0])/steplength;i++){ for(j=0;j<FuncNumber;j++)Auxiliary[j]=*(Yn[j]+i);rightf

9、unctions(x[i],Auxiliary,Func); for(j=0;j<FuncNumber;j++) {K[j][0]=Func[j]; Auxiliary[j]=*(Yn[j]+i)+0.5*steplength*K[j][0];}rightfunctions(x[i],Auxiliary,Func);for(j=0;j<FuncNumber;j++){K[j][1]=Func[j]; Auxiliary

10、[j]=*(Yn[j]+i)+0.5*steplength*K[j][1];} rightfunctions(x[i],Auxiliary,Func); for(j=0;j<FuncNumber;j++){K[j][2]=Func[j]; Auxiliary[j]=*(Yn[j]+i)+steplength*K[j][2];}rightfunctions(x[i],Auxiliary,Func); for(j=0;j<Fu