Metode Numerice

MET BISEC POL

#include <stdio.h>

#include <conio.h>

#include <math.h>

double valpol(int n,double A[10],double x)

{

int i;

double b;

b=A[n];

for(i=n-1;i>=0;i--)

b=A[i]+x*b;

return b;

}

main()

{

int n;

double A[10];

double i,ls,ld,er,xm,*r;

printf("neroarea:");

scanf("%lf",&er);

printf("ngrad:");

scanf("%d",&n);

printf("nlim st:");

scanf("%lf",&ls);

printf("nlim dr:");

scanf("%lf",&ld);

for(i=0;i<=n;i++)

{

printf("ndati coef[%d]:",i);

scanf("%lf",&A[i]);

printf("nA[i]");

}

if(valpol(n,A,ls)*valpol(n,A,ld)>0)

{

printf("err");

getche();

return 0;

}

if(valpol(n,A,ls)==0)

{

*r=ls;

return 1;

}

if(valpol(n,A,ld)==0)

{

*r=ld;

return 1;

}

xm=(ls+ld)/2;

while((fabs(ld-ls)>er)&&(valpol(n,A,xm)!=0))

{

xm=(ls+ld)/2;

if(valpol(n,A,xm)*valpol(n,A,ls)<0)

ld=xm;

else ls=xm;

}

*r=xm;

printf("nradacina:%lf",*r);

getche();

return 1;

}

MET BISEC ECT

#include<conio.h>

#include<stdio.h>

#include<math.h>

double f(double x)

{

return exp(x)-1/x;

}

double der(double x)

{

return 2*x+1.5857;

}

int bisectie(/*double(*f)(double),*/double ls,double ld,double err,double *sol)

{

double xm;

if(f(ls)*f(ld)>0)

return 0;

if(f(ls)==0)

{

*sol=ls;

return 1;

}

if(f(ld)==0)

{

*sol=ld;

return 1;

}

xm=(ls+ld)/2;

while((fabs(ld-ls)>err)&&(f(xm)!=0))

{

xm=(ls+ld)/2;

if(f(ls)*f(xm)<0)

ld=xm;

else ls=xm;

}

*sol=xm;

return 1;

}

main()

{

int e;

double ls,ld,err,*sol;

clrscr();

printf("limst:");

scanf("%lf",&ls);

printf("limdr:");

scanf("%lf",&ld);

printf("eroarea:");

scanf("%lf",&err);

e=bisectie(ls,ld,err,sol);

printf("sol:%lf",*sol);

getche();

return e;

}

MET APROX SUCC

#include <conio.h>

#include <math.h>

double *sol;

double fi (double x)

{

return (-x)*x+2;

}

double Derf(double x)

{

return (-2)*x;

}

/*Functia calculeaza radacina unei ecuatii prin metoda aproximatiilor succesive.

Functia intoarce 0 cand se gaseste radacina cu aproximatia dorita

1 cand nu se indeplinneste conditia de convergenta 2 cand nu se atinge precizia in numarul de pasi impus*/

int AproxSuc (double ls, double ld,

double x0, double err,double NMax, double *sol)

{

double xn,xn_1,pct,pas=0.001;

int iter,sem=1;

pct=ls;

do { xn=Derf(pct);

if ((Derf(pct))>=1) sem=0;

else pct+=pas;

}

while ((sem==1)&&(pct<=ld));

if (sem==0) return 1;

else xn=x0;

iter=1;

do {

xn_1=xn;

xn=fi(xn_1);

iter++;

}

while((fabs(xn-xn_1)>err)&&(iter<=NMax));

*sol=xn;

if (iter<NMax) return 0;

else return 2;

}

main()

{

int i,NMax;

double ls,ld,err,x0;

clrscr();

printf("Calul solutiei unei ecuatii date, cu metoda aproximatiilor succesive.nn");

printf("nIntroduceti eroarea maxima dorita:nn");

scanf("%lf",&err);

printf("nIntroduceti valoarea de start pentru aproximatii:nx0= ");

scanf("%lf",&x0);

printf("nnIntroduceti limitele intervalului in care se cauta solutia:");

printf("nnls= ");

scanf("%lf",&ls);

printf("nld= ");

scanf("%lf",&ld);

printf("nIntroduceti numarul maxim de iteratii:nNMax= ");

scanf("%d",NMax);

printf("n%d",AproxSuc(ls,ld,x0,err,NMax,sol));

printf("Radacina ecuatiei este:t %lf",*sol);

getch();

}

MET NW-RAP ECT

#include <conio.h>

#include <math.h>

double *sol;

double f (double x)

{

return (-x)*x+2;

}

double Derf(double x)

{

return (-2)*x;

}

/*Functia calculeaza radacina unei ecuatii prin metoda Newton-Raphson pentruecuatii transcedente.

Functia intoarce 2 cand derivata este nula 1 cand nu pot afla radacina cu precizia dorita 0 in caz de succes*/

int NewtonRaphsonF (double x0,

double niter,double err,double *sol)

{

double xn,xn_1,aux;

int cont=1;

xn=x0;

do { xn_1=xn;

if ((aux=Derf(xn_1))==0) return 2;

xn=xn_1-f(xn_1)/aux;

cont++;

}

while ((fabs(xn-xn_1)>err)&&(cont<=niter));

if (cont>=niter) return 1;

*sol=xn;

return 0;

}

main()

{

int i,NMax;

double ls,ld,err,x0;

clrscr();

printf("Calul solutiei unei ecuatii date, cu metoda Newton-Raphsonnn");

printf("nIntroduceti eroarea maxima dorita:nn");

scanf("%lf",&err);

printf("nIntroduceti valoarea de start pentru aproximatii:nx0= ");

scanf("%lf",&x0);

printf("nIntroduceti numarul maxim de iteratii:nNMax= ");

scanf("%d",NMax); printf("n%d",NewtonRaphsonF(x0,NMax,err,sol));

printf("Radacina ecuatiei este:t %lf",*sol);

getch();

}