C++을 이용한 근찾기 문제를 위한 이분법 및 할선법, 가위치법, 뉴튼-랩슨법, Aitken 델타제곱법, 뮬러법의 비교

목차

1. 서론
2. 본론
1) 이분법
2) 할선법
3) 가위치법
4) 뉴튼-랩슨법
5) Aitken 델타제곱법
6) 뮬러
3. 결론
4. 별지
5. 소스 및 결과

본문내용

\na%i=%.10f", n, a);
printf("\tb%i=%.10f", n, b);
printf("\tp%i=%.10f", n, p3);
printf("\tf(p%i)=%.10f", n, f(p3));
z=sqrt(pow(p3-p2,2));
p0=p1;
p1=p2;
p2=p3;
}
}
double f(double x)
{
return(pow(x,2)-3);
}
6.3 뮬러법 e^x-3x^2 [0, 1] 10^-8
#include < stdio.h >
#include < math.h >
void Muller_Method(double, double, double, double);
double f(double);
void main(void)
{
printf("e^x-3x^2, [0,1], 10^-8");
double p0, p1, p2, er;
p0=0;
p1=0.5;
p2=1;
er=pow(10, -8);
Muller_Method(p0, p1, p2, er);
}
void Muller_Method(double p0, double p1, double p2, double er)
{
double p3, c, b, a, z;
p3=0;
c=0;
b=0;
a=0;
z=1;
int n=2;
for(;er*100 {
n=n+1;
c=f(p2);
b=(pow((p0-p2),2)*(f(p1)-f(p2))-pow((p1-p2),2)*(f(p0)-f(p2)))/((p0-p2)*(p1-p2)*(p0-p1));
a=((p1-p2)*(f(p0)-f(p2))-((p0)-(p2))*(f(p1)-f(p2)))/((p0-p2)*(p1-p2)*(p0-p1));
p3=p2-(2*c)/((b+sin(b)*sqrt(pow(b,2)-4*a*c)));
printf("\na%i=%.10f", n, a);
printf("\tb%i=%.10f", n, b);
printf("\tp%i=%.10f", n, p3);
printf("\tf(p%i)=%.10f", n, f(p3));
z=sqrt(pow(p3-p2,2));
p0=p1;
p1=p2;
p2=p3;
}
}
double f(double x)
{
return(pow(2.718281828,x)-3*pow(x,2));
}
6.4 뮬러법 e^x-3x^2 [3, 5] 10^-8
#include < stdio.h >
#include < math.h >
void Muller_Method(double, double, double, double);
double f(double);
void main(void)
{
printf("e^x-3x^2, [3,5], 10^-8");
double p0, p1, p2, er;
p0=3;
p1=4;
p2=5;
er=pow(10, -8);
Muller_Method(p0, p1, p2, er);
}
void Muller_Method(double p0, double p1, double p2, double er)
{
double p3, c, b, a, z;
p3=0;
c=0;
b=0;
a=0;
z=1;
int n=2;
for(;er*100 {
n=n+1;
c=f(p2);
b=(pow((p0-p2),2)*(f(p1)-f(p2))-pow((p1-p2),2)*(f(p0)-f(p2)))/((p0-p2)*(p1-p2)*(p0-p1));
a=((p1-p2)*(f(p0)-f(p2))-((p0)-(p2))*(f(p1)-f(p2)))/((p0-p2)*(p1-p2)*(p0-p1));
p3=p2-(2*c)/((b+sin(b)*sqrt(pow(b,2)-4*a*c)));
printf("\na%i=%.10f", n, a);
printf("\tb%i=%.10f", n, b);
printf("\tp%i=%.10f", n, p3);
printf("\tf(p%i)=%.10f", n, f(p3));
z=sqrt(pow(p3-p2,2));
p0=p1;
p1=p2;
p2=p3;
}
}
double f(double x)
{
return(pow(2.718281828,x)-3*pow(x,2));
}
6.5 뮬러법 g/2w^2(e^wt-e^-wt/2-sinwt-1.7 [-0.5,-0.1] 10^-8
#include < stdio.h >
#include < math.h >
void Muller_Method(double, double, double, double);
double f(double);
void main(void)
{
printf("g/2w^2(e^wt-e^-wt/2-sinwt-1.7), [-0.5,-0.1], 10^-8");
double p0, p1, p2, er;
p0=-0.4;
p1=-0.3;
p2=-0.2;
er=pow(10, -8);
Muller_Method(p0, p1, p2, er);
}
void Muller_Method(double p0, double p1, double p2, double er)
{
double p3, c, b, a, z;
p3=0;
c=0;
b=0;
a=0;
z=1;
int n=2;
for(;er*100 {
n=n+1;
c=f(p2);
b=(pow((p0-p2),2)*(f(p1)-f(p2))-pow((p1-p2),2)*(f(p0)-f(p2)))/((p0-p2)*(p1-p2)*(p0-p1));
a=((p1-p2)*(f(p0)-f(p2))-((p0)-(p2))*(f(p1)-f(p2)))/((p0-p2)*(p1-p2)*(p0-p1));
p3=p2-(2*c)/((b+sin(b)*sqrt(pow(b,2)-4*a*c)));
printf("\na%i=%.10f", n, a);
printf("\tb%i=%.10f", n, b);
printf("\tp%i=%.10f", n, p3);
printf("\tf(p%i)=%.10f", n, f(p3));
z=sqrt(pow(p3-p2,2));
p0=p1;
p1=p2;
p2=p3;
}
}
double f(double x)
{
return((-32.17/(2*pow(x,2)))*((pow(2.718281828,x)-pow(2.718281828,-x))/2-sin(x))-1.7);
}

키워드

이분법,   할선법,   가위치법,   뉴턴법,   Aitken,   뮬러법,   소스,   c++