Χρήστης:Theofiloskoss/Project
Αριθμητική Ολοκλήρωση
Η αριθμητική Ολοκλήρωση στην εργασία γίνεται με :
- Απλο Κανόνα Τραπεζίου
- Σύνθετο κανόνα Τραπεζίου
- Απλό κανόνα του Simpson
- Σύνθετο κανόνα του Simpson
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
void aptrap();
void strap();
void apsim();
void ssim();
int main(){
int epil;
printf(" \n\n*********************************** ");
printf(" \n\n ARITHMITIKH ANALYSH ");
printf(" \n\n EARINO E3AMHNO 2009 ");
printf(" 23 IOUNIOY 2009 \n\n");
printf("*********************************** ");
printf(" \n\n APITHMHTIKH OLOKLHRWSH \n\n\n\n");
printf(" EPILOGES \n\n");
printf(" 1. APLOS KANONAS TRAPEZIOY \n");
printf(" 2. SYNTHETOS KANONAS TRAPEZIOY \n");
printf(" 3. APLOS KANONAS TOY SIMPSON \n");
printf(" 4. SYNTHETOS KANONAS TOU SIMPSON \n");
printf(" ALLH EPILOGH --> E3ODOS \n");
printf("\n\n DWSE EPILOGH ");
scanf("%d",&epil);
switch(epil){
case 1 : aptrap();
break;
case 2 : strap();
break;
case 3 : apsim();
break;
case 4 : ssim();
break;
}
return 0;
}
void aptrap(){
float fa,fb,h,trap;
printf(" APLOS KANONAS TRAPEZIOU \n");
printf("DWSE TO f(a): ");
scanf("%f",&fa);
printf("DWSE TO f(b): ");
scanf("%f",&fb);
printf("DWSE TO h: ");
scanf("%f",&h);
trap=(h/2)*(fa+fb);
printf ("TO APOTELESMA EINAI %f: ",trap);
system("pause");
}
void strap(){
int n,i;
float trap,sum=0,h;
float *times_sunartisis;
printf(" SYNTHETOS KANONAS TRAPEZIOY \n");
printf(" DWSE TON ARITHMO TWN STOIXEIWN ");
scanf("%d",&n);
times_sunartisis=malloc(n*sizeof(float));
if(!times_sunartisis){
printf(" Sfalma kata tin dhmiourgia tou Pinaka\n");
printf("to programma termatizei\n");
exit(-1);
}
printf(" APODWSH STOIXEIWN \n");
for(i=0;i<n;i++){
printf("DWSE TO f(X%d)\n",i);
scanf("%f",×_sunartisis[i]);
}
printf("DWSE TO h: ");
scanf("%f",&h);
for(i=1;i<n-2;i++){
sum=sum+times_sunartisis[i];}
trap=(h/2)*(times_sunartisis[0]+times_sunartisis[n-1]+sum);
printf ("TO APOTELESMA EINAI %f: ",trap);
system("pause");
}
void apsim(){
float a,b,fa,fb,fab2,sim;
printf(" APLOS KANONAS TOY SIMPSON \n");
printf(" DWSE TO a");
scanf("%f",&a);
printf(" DWSE TO b");
scanf("%f",&b);
printf(" DWSE TO f(a)");
scanf("%f",&fa);
printf(" DWSE TO f(b)");
scanf("%f",&fb);
printf(" DWSE TO f(a+b)/2");
scanf("%f",&fab2);
sim =((b-a)/6)*(fa+4*fab2+fb);
printf ("TO APOTELESMA EINAI %f: ",sim);
system("pause");
}
void ssim(){
int n,i;
float sim,sum1=0,sum2=0,h,a,b;
float *f;
printf(" \n SYNTHETOS KANONAS TOU SIMPSON \n");
printf("DWSE TO DIASTHMA\n");
printf("A:");
scanf("%f",&a);
printf("B:");
scanf("%f",&b);
printf(" DWSE TON ARITHMO TWN STOIXEIWN (PREPEI NA EINAI PERITOS ARITHMOS)");
scanf("%d",&n);
f = malloc(n*sizeof(float));
if(!f){
printf(" Sfalma kata tin dhmiourgia tou Pinaka\n");
printf("to programma termatizei\n");
exit(-1);
}
h=(b-a)/(n-1);
printf(" APODWSH STOIXEIWN \n");
for(i=0;i<n;i++){
printf("DWSE TO f(%5.3f)\n",a);
scanf("%f",&f[i]);
a=a+h;
}
for(i=1;i<=n-2;i=i+2){
sum1=sum1+f[i];
}
for(i=2;i<=n-3;i=i+2){
sum2=sum2+f[i];
}
sim=(h/3)*(f[0]+f[n-1]+4*sum1+2*sum2);
printf ("TO APOTELESMA EINAI %f: ",sim);
system("pause");
}
Διαφορικές Εξισώσεις
Οι διαφορικές εξισώσεις επιλύονται με:
- Μέθοδο Euler
- Μέθοδο Heun
- Μέθοδο Runge-kutta τέταρτης τάξης (στην εργασία γίνεται στην εξίσωση 2x-y)
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
void euler();
void heun();
void runge_kutta();
float f(float x,float y);
int main(){
int epil;
printf(" \n\n*********************************** ");
printf(" \n\n ARITHMITIKH ANALYSH ");
printf(" \n\n EARINO E3AMHNO 2009 ");
printf(" 22 IOUNIOY 2009 \n\n");
printf("*********************************** ");
printf(" \n\n SYNHTHEIS DIAFORIKES E3ISWSEIS \n");
printf(" PROBLHMA ARXIKWN TIMWN \n\n\n\n");
printf(" EPILOGES \n\n");
printf(" 1. METHODOS Euler \n");
printf(" 2. METHODOS Heun \n");
printf(" 3. METHODOS Runge-kutta 4hs TA3HS \n");
printf(" ALLH EPILOGH --> E3ODOS \n");
printf("\n\n DWSE EPILOGH ");
scanf("%d",&epil);
switch(epil){
case 1 : euler();
break;
case 2 : heun();
break;
case 3 : runge_kutta();
break;
}
return 0;
}
void euler(){
float x,y,h,xn,dy;
int i,n;
printf(" \n\n METHODOS Euler\n\n \n");
printf(" DWSE TO Xo: ");
scanf("%f",&x);
printf(" DWSE TO f(Xo): ");
scanf("%f",&y);
printf(" DWSE TO ALLO AKRO TOY ");
scanf("%f",&xn);
printf(" DWSE TO h: ");
scanf("%f",&h);
n=(int)((xn-x)/h+0.5);
printf("\n\n BHMA X Y\n");
printf("---------------------------\n");
for(i=1;i<=n;i++){
dy = h*f(x,y);
x=x+h;
y=y+dy;
printf(" %d %f %f\n",i,x,y);
}
system("pause");
}
void heun(){
float x,y,h,xn,dy,dy2;
int i,n;
printf(" \n\n METHODOS Heun\n\n \n");
printf(" DWSE TO Xo: ");
scanf("%f",&x);
printf(" DWSE TO f(Xo): ");
scanf("%f",&y);
printf(" DWSE TO ALLO AKRO TOY ");
scanf("%f",&xn);
printf(" DWSE TO h: ");
scanf("%f",&h);
n=(int)((xn-x)/h+0.5);
printf("\n\n BHMA X Y\n");
printf("---------------------------\n");
for(i=1;i<=n;i++){
dy = y+h*f(x,y);
dy2 =y+(h/2)*(f(x,y)+f((x+h),(dy)));
x=x+h;
y=dy2;
printf(" %d %f %f \n",i,x,y);
}
system("pause");
}
void runge_kutta(){
float x,y,h,xn,k1,k2,k3,k4,dy;
int i,n;
printf(" \n\n METHODOS Runge-kutta 4hs TA3HS\n\n \n");
printf(" DWSE TO Xo: ");
scanf("%f",&x);
printf(" DWSE TO f(Xo): ");
scanf("%f",&y);
printf(" DWSE TO ALLO AKRO TOY ");
scanf("%f",&xn);
printf(" DWSE TO h: ");
scanf("%f",&h);
n=(int)((xn-x)/h+0.5);
printf("\n\n BHMA X Y\n");
printf("---------------------------\n");
for(i=1;i<=n;i++){
k1=f(x,y);
k2=f((x+(h/2)),(y+(h/2)*k1));
k3=f((x+(h/2)),(y+(h/2)*k2));
k4=f((x+(h/2)),(y+(h*k3)));
dy =y+(h/6)*(k1+2*k2+2*k3+k4);
x=x+h;
y=dy;
printf(" %d %f %f\n",i,x,y);
}
system("pause");
}
float f(float x,float y){
return(2*x-y);
}
Επίλυση μη γραμμικών εξισώσεων
H επίλυση μη γραμμικών εξισώσεων στην εργασία γίνεται με :
- Μέθοδο διχοτόμησης
- Μέθοδο Newton-Raphson
- Μέθοδο χορδής
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
void dixotomisi();
void newton_raphson();
void xordi();
float synartisi(float);
float paragwgos(float);
int main(){
int epil;
printf(" \n\n********************************** ");
printf(" \n\n ARITHMITIKH ANALYSH ");
printf(" \n\n EARINO E3AMHNO 2009 ");
printf(" 22 IOUNIOY 2009 \n\n");
printf("********************************** ");
printf(" \n\n EPILYSH MH GRAMMIKWN E3ISWSEWN \n\n\n");
printf(" EPILOGES \n\n");
printf(" 1. METHODOS DOXOTOMISIS \n");
printf(" 2. METHODOS NEWTON - RAPHSON \n");
printf(" 3. METHODOS XORDHS \n");
printf(" ALLH EPILOGH --> E3ODOS \n");
printf("\n\n DWSE EPILOGH ");
scanf("%d",&epil);
switch(epil){
case 1 : dixotomisi();
break;
case 2 : newton_raphson();
break;
case 3 : xordi();
break;
}
return 0;
}
void dixotomisi(){
int al=1;
float fa,fb,a,b,x,fx,e=0.0001;
printf(" METHODOS DOXOTOMISIS \n");
printf("DWSE TO a: ");
scanf("%f",&a);
printf("DWSE TO b: ");
scanf("%f",&b);
x=(a+b)/2;
fa=synartisi(a);
fb=synartisi(b);
fx=synartisi(x);
if ((fa*fb)<0){
while(al=1){
fx=synartisi(x);
if ((fabs(b-a)/2)<=e){
printf("H riza einai: %f ",x);
al=0;
system("pause");
break;
}
if((fa*fx)<0){
printf(" %f %f %f %f %f \n",a,b,fa,fb,x);
b=x;
fb=synartisi(b);}
else{
printf(" %f %f %f %f %f \n",a,b,fa,fb,x);
a=x;
fa=synartisi(a);
}
x=(a+b)/2; }
fa=synartisi(a);
fb=synartisi(b);
fx=synartisi(x);
printf(" %f %f %f %f %f \n",a,b,fa,fb,x);
}
exit(0);
}
void newton_raphson(){
int al=1;
float fa,fp,fb,b,a,e=0.001;
printf(" \n\nMETHODOS NEWTON - RAPHSON \n");
printf("\nDWSE THN ARXIKH PROSEGGISH: ");
scanf("%f",&a);
fa=synartisi(a);
fp=paragwgos(a);
b = a -(fa/fp);
fb=synartisi(b);
printf("\n Xo f(Xo) f'(Xo) X1 f(X1)");
printf("\n%f %f %f %f %f \n",a,fa,fp,b,fb);
do
{
if (fb<e){
printf("\nH riza einai: %f \n",b);
system("pause");
break;}
else{
a=b;
fa=synartisi(a);
fp=paragwgos(a);
b=a-(fa/fp);
fb=synartisi(b);
printf("%f %f %f %f %f \n",a,fa,fp,b,fb);
}
}while(al=1);
}
void xordi(){
int al=1;
float fa,fc,fb,b,a,c,e=0.00001;
printf(" \n\nMETHODOS XORDHS \n");
printf("\nDWSE THN PRWTH ARXIKH PROSEGGISH: ");
scanf("%f",&a);
printf("\nDWSE THN DEUTERH ARXIKH PROSEGGISH: ");
scanf("%f",&b);
fa=synartisi(a);
fb=synartisi(b);
c=((a*fb-b*fa)/(fb-fa));
fc=synartisi(c);
printf("\n Xo X1 f(Xo) f(X1) X2 f(X2)");
printf("\n%f %f %f %f %f %f\n",a,fa,b,fb,c,fc);
do
{
if (fabs(fc)<e){
printf("\nH riza einai: %f \n",c);
system("pause");
break;}
else{
a=b;
b=c;
fa=synartisi(a);
fb=synartisi(b);
c=((a*fb-b*fa)/(fb-fa));
fc=synartisi(c);
printf("%f %f %f %f %f %f\n",a,fa,b,fb,c,fc);
}
}while(al=1);
}
float synartisi(float x){
float y;
y= x*x-25;
return(y);
}
float paragwgos(float x){
float y;
y = 3*x*x-2;
return(y);
}