计算方法上机实验_计算方法上机实验1
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龙格-库塔
#include
#include
float function(float x,float y)
{
return(0-(y*y));//f(x,y)µÄ±í´ïʽ }
int main()
{
float x0,x1,y0,y1,k1,k2,k3,k4,a,b,c,n,h;int i;
scanf(“%f %f %f %f”,&a,&b,&c,&n);x0=a;
y0=c;
h=(b-a)/n;
for(i=1;i
{
k1=h*function(x0,y0);
k2=h*function(x0+h/2,y0+k1/2);k3=h*function(x0+h/2,y0+k2/2);k4=h*function(x0+h,y0+k3);x1=x0+h;
y1=y0+(k1+2*k2+2*k3+k4)/6;
printf(“x%d=%f,y%d=%fn”,i,x1,i,y1);x0=x1;
y0=y1;
}
return 0;
}
拉格朗日
#include
#include
#include
#define maxlength 500
#define pi 3.14***
floata[maxlength],f[maxlength];
float n;
floatlagrange(floata[],floatf[],float x,int n)
{
int k=0,j;
floaty=0.0,l;
while(k
{
l=1.0;
// printf(“%lfn”,y);
for(j=0;j
{
if(j!=k)
{
l=l*(x-a[j])/(a[k]-a[j]);// printf(“%lfn”,l);
}
}
//printf(“%lfn”,f[k]);
// printf(“%lfn”,l);
y=y+l*f[k];
k++;
}
printf(“x=%f,y=%fn”,x,y);
return y;
}
float fx1(floatx)
{
return(1/(1+x*x));
}
floatfx2(floatx)
{
return exp(x);
}
floatfx3(float x)
{
return sqrt(x);
}
void math1(float c,float n)
{
int i=0;
float h;
h=2*c/n;
while(i
{
a[i]=i*h-5;
i++;
}
}
void math2()
{
int i=0;
while(i
{
a[i]=cos((2*i+1)*pi/2/(n+1));
i++;
}
}
int main()
{
n=20;
int i;
math1(5,n);
for(i=0;i
{
f[i]=fx1(a[i])
}
lagrange(a,f,0.75,n);
return 0;
}
龙贝格
#include
#include
#include
double t[1000],r[1000];
double f(double x)
{
return(x*x*exp(x));
}
int main()
{
double h,a,b,e;
int i,N,m;
scanf(“%lf,%lf,%d,%lf”,&a,&b,&N,&e);
h=b-a;
m=0;
t[1]=0.5*h*(f(a)+f(b));
printf(“%lf”,t[1]);
r[0]=t[0];
while(1)
{
printf(“n”);
for(i=0;i
t[i]=r[i];
m++;
h=h/2;
r[0]=t[0]/2;
for(i=1;i
r[0]+=h*f(a+(i-0.5)*h)/2;
printf(“%lf”,r[0]);
r[1]=(4*r[0]-t[0])/3;
printf(“ %lf”,r[1]);
if(m==1)
continue;
r[2]=(16*r[1]-t[1])/15;
printf(“ %lf”,r[2]);
if(m==2)
continue;
r[3]=(64*r[2]-t[2])/63;
printf(“ %lf”,r[3]);
if(m==3)
continue;
if((fabs(r[3]-t[3])
break;
}
printf(“nthe current time is :%dn”,m);
return 0;
}
牛顿
#include
#include
#include
double function(double point)
{
return(point*point-2*point*exp(-point)+exp(-2*point));
}
double d_function(double point)
{
return(2*point+2*point*exp(-point)-2*exp(-point)-2*exp(-2*point));}
int main()
{
double beginner,error1,error2;
int max_times=0;
beginner=error1=error2=0;
scanf(“%lf %lf %lf %d”,&beginner,&error1,&error2,&max_times);int current_times=0;
while(current_times
{
if(fabs(function(beginner))
{
printf(“%lfn”,beginner);
return 0;
}
if(fabs(d_function(beginner))
{
printf(“failuren”);
return 0;
}
beginner=beginner-function(beginner)/d_function(beginner);if(fabs(function(beginner)/d_function(beginner))
printf(“%lfn”,beginner);
return 0;
}
current_times++;
}
printf(“failuren”);
return 0;
}
