#include<stdio.h> #include<conio.h> #include<math.h> void main() { float x[10],y[10],temp=1,f[10],sum,p; int i,n,j,k=0,c; clrscr(); printf("\nhow many record you will be enter: "); scanf("%d",&n); for(i=0; i<n; i++) { printf("\n\nenter the value of x%d: ",i); scanf("%f",&x[i]); printf("\n\nenter the value of f(x%d): ",i); scanf("%f",&y[i]); } printf("\n\nEnter f(x) for finding x: "); scanf("%f",&p); for(i=0;i<n;i++) { temp = 1; k = i; for(j=0;j<n;j++) { if(k==j) { continue; } else { temp = temp * ((p-y[j])/(y[k]-y[j])); } } f[i]=x[i]*temp; } for(i=0;i<n;i++) { sum = sum + f[i]; } printf("\n\n* * * x = %f * * *",sum); getch(); } ------------------------OUT PUT------------------------- how many record you will be enter: 4 enter the value of x0: 20 enter the value of f(x0): 0.342 enter the value of x1: 25 enter the value of f(x1): 0.423 enter the value of x2: 30 enter the value of f(x2): 0.500 enter the value of x3: 35 enter the value of f(x3): 0.650 Enter f(x) for finding x: 0.390 * * * x = 22.840574 * * *
Tuesday 18 November 2014
LAGRANGE'S INTERPOLATION Method For Finding X in C
RUNGE-KUTTA Method in C
#include<stdio.h> #include <math.h> #include<conio.h> //dy/dx = y - x#define F(x,y) (y)-(x) void main() { double y0,x0,y1,n,h,f,f1,k1,k2; int j; clrscr(); printf("\nEnter the value of x0: "); scanf("%lf",&x0); printf("\nEnter the value of y0: "); scanf("%lf",&y0); printf("\nEnter the value of h: "); scanf("%lf",&h); printf("\nEnter the value of last point: "); scanf("%lf",&n); for(; x0<n; x0=x0+h) { f=F(x0,y0); k1 = h * f; f1 = F(x0+h,y0+k1); k2 = h * f1; y1 = y0 + ( k1 + k2)/2; printf("\n\n k1 = %.4lf ",k1); printf("\n\n k2 = %.4lf ",k2); printf("\n\n y(%.4lf) = %.3lf ",x0+h,y1); y0=y1; } getch(); } ------------------------OUT PUT---------------------- Enter the value of x0: 0 Enter the value of y0: 2 Enter the value of h: 0.05 Enter the value of last point: 0.1 k1 = 0.1000 k2 = 0.1025 y(0.0500) = 2.101 k1 = 0.1026 k2 = 0.1052 y(0.1000) = 2.205
NEWTON'S BACKWARD DIFFERENCE INTERPOLATION Method in C
#include<stdio.h> #include<conio.h> #define MAX 10 int factorial(intvalue); void main() { FILE *fp; int number,i,j,k=0,m; float xvalue[MAX],yvalue[MAX],search; float differ[MAX][MAX],uvalue,hvalue,product,sum; fp=fopen("nwbdi.dat","w"); clrscr(); printf("\n\n"); fprintf(fp,"\n\n"); printf("How many numbers you want to enter for x : "); fprintf(fp,"How many numbers you want to enter for x : "); scanf("%d",&number); fprintf(fp,"%d",number); for(i=0;i<number;i++) { printf("\nEnter value for x(%d) : ",i); fprintf(fp,"\nEnter value for x(%d) : ",i); scanf("%f",&xvalue[i]); fprintf(fp,"%f",xvalue[i]); printf("\nEnter value for y(%d) : ",i); fprintf(fp,"\nEnter value for y(%d) : ",i); scanf("%f",&yvalue[i]); fprintf(fp,"%f",yvalue[i]); } printf("\nEnter any value of x for which you want to find y : "); fprintf(fp,"\nEnter any value of x for which you want to find y : "); scanf("%f",&search); fprintf(fp,"%f",search); if(search<xvalue[0] || search>xvalue[number-1]) { printf("\n\nValue lies outside the given values of x "); fprintf(fp,"\n\nValue lies outside the given values of x "); getch(); exit(1); } else { clrscr(); printf("\n\nNEWTON'S BACKWARD DIFFERENCE INTERPOLATION "); fprintf(fp,"\n\nNEWTON'S BACKWARD DIFFERENCE INTERPOLATION "); for(j=0;j<number-1;j++) { for(i=j+1;i<number;i++) { if(j==0) { differ[i][j]=yvalue[i]-yvalue[i-1]; } else { differ[i][j]=differ[i][j-1]-differ[i-1][j-1]; } } } printf("\n\n"); fprintf(fp,"\n\n"); printf(" x y "); fprintf(fp," x y "); for(i=1;i<number;i++) { printf(" d^%dy(i) ",i); fprintf(fp," d^%dy(i) ",i); } printf("\n\n"); fprintf(fp,"\n\n"); for(i=0;i<number;i++) { printf(" %.2f %.2f ",xvalue[i],yvalue[i]); fprintf(fp," %.2f %.2f ",xvalue[i],yvalue[i]); for(j=0;j<i;j++) { printf(" %.4f ",differ[i][j]); fprintf(fp," %.4f ",differ[i][j]); } printf("\n"); fprintf(fp,"\n"); } for(i=0;i<number;i++) { if(search>xvalue[i]) { k=k+1; } } hvalue=xvalue[1]-xvalue[0]; uvalue=(search-xvalue[k])/hvalue; sum=yvalue[k]; for(i=0;i<number-1 ;i++) { product=1; for(j=0;j<=i;j++) { product=product*(uvalue+j); } m=factorial(i+1); sum=sum+(differ[k][i]*product)/m; } printf("\n\n"); printf("Interpolated value is : %f ",sum); fprintf(fp,"Interpolated value is : %f ",sum); } fclose(fp); getch(); } int factorial(intvalue) { int i,temp=1; for(i=value;i>=1;i--) { temp=temp*i; } return(temp); }
NEWTON'S FORWARD DIFFERENCE Method in C
#include<stdio.h> #include<conio.h> #include<math.h> void main() { float x[10],y[10][10],sum,p,u,temp; int i,n,j,k=0,f,m; float fact(int); clrscr(); printf("\nhow many record you will be enter: "); scanf("%d",&n); for(i=0; i<n; i++) { printf("\n\nenter the value of x%d: ",i); scanf("%f",&x[i]); printf("\n\nenter the value of f(x%d): ",i); scanf("%f",&y[k][i]); } printf("\n\nEnter X for finding f(x): "); scanf("%f",&p); for(i=1;i<n;i++) { for(j=0;j<n-i;j++) { y[i][j]=y[i-1][j+1]-y[i-1][j]; } } printf("\n_____________________________________________________\n"); printf("\n x(i)\t y(i)\t y1(i) y2(i) y3(i) y4(i)"); printf("\n_____________________________________________________\n"); for(i=0;i<n;i++) { printf("\n %.3f",x[i]); for(j=0;j<n-i;j++) { printf(" "); printf(" %.3f",y[j][i]); } printf("\n"); } i=0; do { if(x[i]<p && p<x[i+1]) k=1; else i++; }while(k != 1); f=i; u=(p-x[f])/(x[f+1]-x[f]); printf("\n\n u = %.3f ",u); n=n-i+1; sum=0; for(i=0;i<n-1;i++) { temp=1; for(j=0;j<i;j++) { temp = temp * (u - j); } m=fact(i); sum = sum + temp*(y[i][f]/m); } printf("\n\n f(%.2f) = %f ",p,sum); getch(); } float fact(int a) { float fac = 1; if (a == 0) return (1); else fac = a * fact(a-1); return(fac); } ------------------------OUT PUT----------------------- how many record you will be enter: 5 enter the value of x0: 2 enter the value of f(x0): 9 enter the value of x1: 2.25 enter the value of f(x1): 10.06 enter the value of x2: 2.5 enter the value of f(x2): 11.25 enter the value of x3: 2.75 enter the value of f(x3): 12.56 enter the value of x4: 3 enter the value of f(x4): 14 Enter X for finding f(x): 2.35 _____________________________________________________ x(i) y(i) y1(i) y2(i) y3(i) y4(i) _____________________________________________________ 2.000 9.000 1.060 0.130 -0.010 0.020 2.250 10.060 1.190 0.120 0.010 2.500 11.250 1.310 0.130 2.750 12.560 1.440 3.000 14.000 u = 0.400 f(2.35) = 10.522240
NEWTON RAPHSON Method in C
#include<conio.h> #include<stdio.h> #include<stdlib.h> #include<math.h> int user_power,i=0,cnt=0,flag=0; int coef[10]={0}; float x1=0,x2=0,t=0; float fx1=0,fdx1=0; void main() { clrscr(); printf("\n\n\t\t\t PROGRAM FOR NEWTON RAPHSON GENERAL"); printf("\n\n\n\tENTER THE TOTAL NO. OF POWER:::: "); scanf("%d",&user_power); for(i=0;i<=user_power;i++) { printf("\n\t x^%d::",i); scanf("%d",&coef[i]); } printf("\n"); printf("\n\t THE POLYNOMIAL IS ::: "); for(i=user_power;i>=0;i--)//printing coeff. { printf(" %dx^%d",coef[i],i); } printf("\n\tINTIAL X1---->"); scanf("%f",&x1); printf("\n ******************************************************"); printf("\n ITERATION X1 FX1 F'X1 "); printf("\n **********************************************************"); do { cnt++; fx1=fdx1=0; for(i=user_power;i>=1;i--) { fx1+=coef[i] * (pow(x1,i)) ; } fx1+=coef[0]; for(i=user_power;i>=0;i--) { fdx1+=coef[i]* (i*pow(x1,(i-1))); } t=x2; x2=(x1-(fx1/fdx1)); x1=x2; printf("\n %d %.3f %.3f %.3f ",cnt,x2,fx1,fdx1); }while((fabs(t - x1))>=0.0001); printf("\n\t THE ROOT OF EQUATION IS %f",x2); getch(); } --------------------------OUTPUT---------------------------- PROGRAM FOR NEWTON RAPHSON GENERAL ENTER THE TOTAL NO. OF POWER:::: 3 x^0::-3 x^1::-1 x^2::0 x^3::1 THE POLYNOMIAL IS ::: 1x^3 0x^2 -1x^1 -3x^0 INTIAL X1---->3 ************************************** ITERATION X1 FX1 F'X1 ************************************** 1 2.192 21.000 26.000 2 1.794 5.344 13.419 3 1.681 0.980 8.656 4 1.672 0.068 7.475 5 1.672 0.000 7.384 ************************************** THE ROOT OF EQUATION IS 1.671700
SECANT Method in C
#include<stdio.h> #include<conio.h> #include<math.h> #define ESP 0.0001 #define F(x) (x)*(x) - 4*(x) - 10 void main() { float x1,x2,x3,f1,f2,t; clrscr(); printf("\nEnter the value of x1: "); scanf("%f",&x1); printf("\nEnter the value of x2: "); scanf("%f",&x2); printf("\n______________________________________________\n"); printf("\n x1\t x2\t x3\t f(x1)\t f(x2)"); printf("\n______________________________________________\n"); do { f1=F(x1); f2=F(x2); x3=x2-((f2*(x2-x1))/(f2-f1)); printf("\n%f %f %f %f %f",x1,x2,x3,f1,f2); x1=x2; x2=x3; if(f2<0) t=fabs(f2); else t=f2; }while(t>ESP); printf("\n______________________________________________\n"); printf("\n\nApp.root = %f",x3); getch(); } ---------------------- OUT PUT ------------------------- Enter the value of x1: 4 Enter the value of x2: 2 ___________________________________________________________ x1 x2 x3 f(x1) f(x2) ___________________________________________________________ 4.000000 2.000000 9.000000 -10.000000 -14.000000 2.000000 9.000000 4.000000 -14.000000 35.000000 9.000000 4.000000 5.111111 35.000000 -10.000000 4.000000 5.111111 5.956522 -10.000000 -4.320987 5.111111 5.956522 5.722488 -4.320987 1.654063 5.956522 5.722488 5.741121 1.654063 -0.143084 5.722488 5.741121 5.741659 -0.143084 -0.004015 5.741121 5.741659 5.741657 -0.004015 0.000010 ___________________________________________________________ App.root = 5.741657
FALSE POSITION Method in C
#include<stdio.h> #include<conio.h> #include<math.h> #define ESP 0.0001 #define F(x) 3*(x) - 1 - cos(x) void main() { float x0,x1,x2,f1,f2,f0; int count=0; clrscr(); do { printf("\nEnter the value of x0: "); scanf("%f",&x0); }while(F(x0) > 0); do { printf("\nEnter the value of x1: "); scanf("%f",&x1); }while(F(x1) < 0); printf("\n__________________________________________________________\n"); printf("\n x0\t x1\t x2\t f0\t f1\t f2"); printf("\n__________________________________________________________\n"); do { f0=F(x0); f1=F(x1); x2=x0-((f0*(x1-x0))/(f1-f0)); f2=F(x2); printf("\n%f %f %f %f %f %f",x0,x1,x2,f0,f1,f2); if(f0*f2<0) { x1=x2; } else { x0 = x2; } }while(fabs(f2)>ESP); printf("\n__________________________________________________________\n"); printf("\n\nApp.root = %f",x2); getch(); } -------------------- OUT PUT -------------------- Enter the value of x0: -1 Enter the value of x1: 1 __________________________________________________________ x0 x1 x2 f0 f1 f2 __________________________________________________________ -1.000000 1.000000 0.513434 -4.540302 1.459698 -0.330761 0.513434 1.000000 0.603320 -0.330761 1.459698 -0.013497 0.603320 1.000000 0.606954 -0.013497 1.459698 -0.000527 0.606954 1.000000 0.607096 -0.000527 1.459698 -0.000021 __________________________________________________________ App.root = 0.607096
Bisection Method in C
#include<stdio.h> #include <math.h> #include<conio.h> #define ESP 0.001 #define F(x) (x)*(x)*(x) + (x)*(x) + (x) + 7 void main() { int i = 1; float x0,x1,x2; double f1,f2,f0,t; clrscr(); printf("\nEnter the value of x0: "); scanf("%f",&x0); printf("\nEnter the value of x1: "); scanf("%f",&x1); printf("\n__________________________________________________________________\n"); printf("\niteration\t x0\t x1\t x2\t f0\t f1\t f2"); printf("\n___________________________________________________________________\n"); do { x2=(x0+x1)/2; f0=F(x0); f1=F(x1); f2=F(x2); printf("\n%d %f %f %f %lf %lf %lf", i, x0,x1,x2,f0,f1,f2); if(f0*f2<0) { x1=x2; } else { x0=x2; } i++; }while(fabs(f2)>ESP); printf("\n__________________________________________________________\n"); printf("\n\nApp.root = %f",x2); getch(); } ----------------------------OUT PUT--------------------------- Enter the value of x0: -2 Enter the value of x0: -1 Enter the value of x1: -2 __________________________________________________________ x0 x1 x2 f0 f1 f2 __________________________________________________________ -1.000000 -2.000000 -1.500000 -5.000000 2.000000 -1.750000 -1.500000 -2.000000 -1.750000 -1.750000 2.000000 0.062500 -1.500000 -1.750000 -1.625000 -1.750000 0.062500 -0.859375 -1.625000 -1.750000 -1.687500 -0.859375 0.062500 -0.402344 -1.687500 -1.750000 -1.718750 -0.402344 0.062500 -0.170898 -1.718750 -1.750000 -1.734375 -0.170898 0.062500 -0.054443 -1.734375 -1.750000 -1.742188 -0.054443 0.062500 0.003967 -1.734375 -1.742188 -1.738281 -0.054443 0.003967 -0.025253 -1.738281 -1.742188 -1.740234 -0.025253 0.003967 -0.010647 -1.740234 -1.742188 -1.741211 -0.010647 0.003967 -0.003341 -1.741211 -1.742188 -1.741699 -0.003341 0.003967 0.000313 __________________________________________________________ App.root = -1.741699
Monday 17 November 2014
TRAPEZOIDAL RULE in C
#include<stdio.h> #include<conio.h> #include<math.h> void main() { float x[10],y[10],sum=0,h,temp; int i,n,j,k=0; float fact(int); clrscr(); printf("\nhow many record you will be enter: "); scanf("%d",&n); for(i=0; i<n; i++) { printf("\n\nenter the value of x%d: ",i); scanf("%f",&x[i]); printf("\n\nenter the value of f(x%d): ",i); scanf("%f",&y[i]); } h=x[1]-x[0]; n=n-1; for(i=0;i<n;i++) { if(k==0) { sum = sum + y[i]; k=1; } else sum = sum + 2 * y[i]; } sum = sum + y[i]; sum = sum * (h/2); printf("\n\n I = %f ",sum); getch(); }
---------------------------- OUTPUT ---------------------------- how many record you will be enter: 6 enter the value of x0: 7.47 enter the value of f(x0): 1.93 enter the value of x1: 7.48 enter the value of f(x1): 1.95 enter the value of x2: 7.49 enter the value of f(x2): 1.98 enter the value of x3: 7.50 enter the value of f(x3): 2.01 enter the value of x4: 7.51 enter the value of f(x4): 2.03 enter the value of x5: 7.52 enter the value of f(x5): 2.06 I = 0.099652
SIMPSON'S 3/8 Method in C
#include<stdio.h> #include<conio.h> #include<math.h> void main() { float x[10],y[10],sum=0,h,temp; int i,n,j,k=0; float fact(int); clrscr(); printf("\nhow many record you will be enter: "); scanf("%d",&n); for(i=0; i<n; i++) { printf("\n\nenter the value of x%d: ",i); scanf("%f",&x[i]); printf("\n\nenter the value of f(x%d): ",i); scanf("%f",&y[i]); } h=x[1]-x[0]; n=n-1; sum = sum + y[0]; for(i=1;i<n;i++) { if(k==0) { sum = sum + 4 * y[i]; k=1; } else { sum = sum + 2 * y[i]; k=0; } } sum = sum + y[i]; sum = sum * (h/3); printf("\n\n I = %f ",sum); getch(); }-------------------------- OUTPUT ----------------------how many record you will be enter: 5 enter the value of x0: 0 enter the value of f(x0): 1 enter the value of x1: 0.25 enter the value of f(x1): 0.8 enter the value of x2: 0.5 enter the value of f(x2): 0.6667 enter the value of x3: 0.75 enter the value of f(x3): 0.5714 enter the value of x4: 1 enter the value of f(x4): 0.5 I = 0.693250
Simpson's 1/3 Method in C
#include<stdio.h> #include<conio.h> #include<math.h> void main() { float x[10],y[10],sum=0,h,temp; int i,n,j,k=0; float fact(int); clrscr(); printf("\nhow many record you will be enter: "); scanf("%d",&n); for(i=0; i<n; i++) { printf("\n\nenter the value of x%d: ",i); scanf("%f",&x[i]); printf("\n\nenter the value of f(x%d): ",i); scanf("%f",&y[i]); } h=x[1]-x[0]; n=n-1; sum = sum + y[0]; for(i=1;i<n;i++) { if(k==0) { sum = sum + 4 * y[i]; k=1; } else { sum = sum + 2 * y[i]; k=0; } } sum = sum + y[i]; sum = sum * (h/3); printf("\n\n I = %f ",sum); getch(); }-------------------------- OUTPUT ----------------------how many record you will be enter: 5 enter the value of x0: 0 enter the value of f(x0): 1 enter the value of x1: 0.25 enter the value of f(x1): 0.8 enter the value of x2: 0.5 enter the value of f(x2): 0.6667 enter the value of x3: 0.75 enter the value of f(x3): 0.5714 enter the value of x4: 1 enter the value of f(x4): 0.5 I = 0.693250
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