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//Write a program to implement bisection method #include<stdio.h> #include<conio.h> #include<math.h> #define max 10 float f(float x); void main() { float a,b,c,d,t; int i,j,n; clrscr(); printf("\nEnter the number of iteration : "); scanf("%d",&n); for(i=-max;i<max;i++) { a=i; b=i+1; if(f(a)f(b)<=0) { if(f(a)>f(b)) {t=a;a=b;b=t;} printf("\nThe initial approximate limits are : "); printf("%f%f",a,b); printf("\n\n a b c f(c)"); for(j=0;j<n;j++) { c=(a+b)/2; printf("\n\n %10.6f %10.6f %10.6f %10.6f",a,b,c,f(c)); if(f(c)<0) a=c;else b=c; } getch(); } } } float f(float x) { return(cos(x)-3x+1);
//Write a program to implement Regular Falsi method #include<stdio.h> #include<conio.h> #include<math.h> float f(float x) { return cos(x) - x*exp(x); } void regula (float *x, float x0, float x1, float fx0, float fx1, int itr) { x = x0 - ((x1 - x0) / (fx1 - fx0))fx0; ++(itr); printf("Iteration no. %3d X = %7.5f \n", *itr, x); } int main () { int itr = 0, maxmitr; float x0,x1,x2,x3,allerr; clrscr(); printf("\nEnter the values of x0, x1, allowed error and maximum iterations:\n"); scanf("%f %f %f %d", &x0, &x1, &allerr, &maxmitr); regula (&x2, x0, x1, f(x0), f(x1), &itr); do { if (f(x0)f(x2) < 0) x1=x2; else x0=x2; regula (&x3, x0, x1, f(x0), f(x1), &itr); if (fabs(x3-x2) < allerr) { printf("After %d iterations, root = %6.4f\n", itr, x3); getch(); return 0; } x2=x3; } while (itr<maxmitr); printf("Solution does not converge or iterations not sufficient:\n"); getch(); return 1;
//Write a program to implement secant method #include<stdio.h> #include<conio.h> #include<math.h> float f(float x) { return(xxx-4); } float main() { float a,b,c,d,e; int count=1,n; clrscr(); printf("\nEnter the values of a and b : "); scanf("%f%f",&a,&b); printf("Enter the values of allowed error and maximum number : "); scanf("%f%d",&e,&n); do { if(f(a)==f(b)) { printf("\nSolution cannot be found as the values of a and b"); return 0; } c=(af(b)-bf(a))/(f(b)-f(a)); a=b; b=c; printf("Iteration No-%d x=%f\n",count,c); count++; if(count==n) { break; } } while(fabs(f(c))>e); printf("\nThe Required solution is %f\n",c); getch();
//Write a program to implement Newton Rapshon method #include<stdio.h> #include<conio.h> #include<math.h> float f(float x) { return(cos(x)-3x+1); } float f1(float y) { return(-sin(y)-3); } void main() { float a,b,c,d; int i,j,n; clrscr(); printf("\nEnter the number of iterations : "); scanf("%d",&n); for(i=-8;i<8;i++) { a=1; b=i+1; if(f(a)f(b)<=0) { printf("\nThe initial approximate value is : "); c=(a+b)/2.0; printf("%f",c); printf("\nn c f(c)"); for(j=0;j<n;j++) { printf("\n%-5d%15.6f%15.6f",j+1,c,f(c)); d=c-(f(c)/f1(c)); c=d; } getch(); } }}
s += mat[i][j]out[j]; } s=mat[i] [n]-s; out[i]=s/mat[i][j]; } for(i=0;i<n;i++) { gotoxy(15i+10,21); printf("%c = %-10.3f",'z'-n+i+1,out[i]); } getch(); getch(); } void matrix(float mat[10][11],int n) { int i=0,j=0; do { if((mat[i][i]!=mat[j][i]) && (mat[i][i]==0) && (j<n)) swap(mat,n,i,j); j++; if(j%n==0) j=++i; }while(i<n); } void swap(float mat[10][11],int n,int r1,int r2) { float temp; int i; for(i=0;i<=n;i++) { temp=mat[r1][i]; mat[r1][i]=mat[r2][i]; mat[r2][i]=temp; }
//Write a program to implement Euler's method #include<stdio.h> #include<conio.h> #include<math.h> float f(float x,float y) { return(yy-xx); } void main() { float h,x,y,y0,x0,y1; clrscr(); printf("\nenter initial approximate x0,y0&interval width h:"); scanf("%f%f%f",&x0,&y0,&h); printf("enter the value of x at which y is required:"); scanf("%f",&x); printf("\n\t x \t y"); do { y=h*f(x0,y0); y1=y+y0; printf("\n%f%f",x0,y1); x0=x0+h; y0=y1; } while(x0<x); getch();
//Write a program to implement Simpson 1/3 rule #include<stdio.h> #include<conio.h> #include<math.h> float f(float x); void main() { float k=0.0,h,x,a,b; int i,n; clrscr(); printf("the function f(x):1/(1+xx)"); printf("\nenter the lower and upper limits="); printf("\na="); scanf("%f",&a); printf("b="); scanf("%f",&b); printf("enter the number of strips(in multiple of '2') = "); scanf("%d",&n); h=(b-a)/(2(n/2)); printf("\n x f(x)"); for(x=a,i=0;x<b;x=x+2h,i=i+2) { k+=f(x)+4f(x+h)+f(x+2h); printf("\n%.6f%15.6f",x,f(x)); printf("\n%.6f%15.6f",x+h,f(x+h)); } printf("\n\nthe definite integral is %15.6f",(h/3.0)k); getch(); } float f(float x) { return(1/(1+x*x));
//Write a program to implement Simpson 3/8 rule #include<stdio.h> #include<conio.h> #include<math.h> float f(float x); void main() { float k=0.0,h,x,a,b; int i,n; clrscr(); printf("the function f(x):1/(1+xx)"); printf("\nenter the lower and upper limits="); printf("\na="); scanf("%f",&a); printf("b="); scanf("%f",&b); printf("enter the number of strips(in multiple of '2') = "); scanf("%d",&n); h=(b-a)/(2(n/2)); printf("\n x f(x)"); for(x=a,i=0;x<b;x=x+3h,i=i++) { k+=f(x)+3f(x+h)+3f(x+2h)+f(x+3h); printf("\n%.6f%15.6f",x,f(x)); printf("\n%.6f%15.6f",x+h,f(x+h)); printf("\n%.6f%15.6f",x+2h,f(x+2h)); } printf("\n %f%15.6f",x,f(x)); printf("\n\nthe definite integral is %15.6f",(3h/8.0)k); getch(); } float f(float x) { return(1/(1+xx));
//Write a program to implement Gauss seidal method #include<stdio.h> #include<conio.h> #include<math.h> int check_matrix(float[10][11],int); void clear(); void main() { float mat[10][11],temp,out[10]={0},ratio,o,s; int i,j,k=0,n,ck,flag; clrscr(); gotoxy(10,3); cprintf("Enter order of matrix : "); cscanf("%d",&n); for(i=0;i<n;i++) for(j=0;j<n+1;j++) { gotoxy(10j+10,i+5); if(j<n)cprintf("%c",'z'-n+j+1); cscanf("%f",&mat[i][j]); gotoxy(16+10j,j+5); if(j<n-1)cprintf("+"); else if(j==n-1)cprintf("="); } ck=check_matrix(mat,n); if(ck==-1) { gotoxy(10,15); cprintf("The given equation are not valid for gauss seidal method"); } gotoxy(10,10); cprintf("A table for gauss seidal method:-"); for(j=0;j<n+1;j++) { gotoxy(5j+3,12); if(j<n)cprintf("%c",'z'-n+j+1); } do { flag=1; if(k%8==0)clear(); for(i=0;i<n;i++) { temp=out[i]; s=0; for(j=0;j<n;j++) { if(j!=1) { s+=out[j]*mat[i][j]; }
out[i]=(mat[i][n]-s)/mat[i][j]; gotoxy(10+15*i,13+k%8); cprintf("%-f",out[i]); if(fabs(temp-out[i])>0.000001)flag=0; } k++; } while(flag==0); getch(); } int check_matrix(float mat[10][11],int n) { int i,j; float sum=0; for(i=0;i<n;i++) { for(j=0;j<n;j++) { if(i!=j)sum+=abs(mat[i][j]/mat[i][j]); } if(sum>1)return-1; } return 0; } void clear() { int i,j; gotoxy(15,22); cprintf("Press any key to see more..."); getch(); for(i=10;i<70;i++) for(j=13;j<21;j++) { gotoxy(i,j); printf(" "); }
for(z=0;x[z]<=x0;z++); u=(float)(x0-x[i])/(x[1]-x[0]); v=u; v1=u-1; t=v1; ans=ans+((y[i]+y[i+2]/2)); z=1; for(j=0;j<n-1;j++) { g=h=g1=h1=1; if(j==0) { if(j%2==0) { u=u(v+g); g++; t=t(v1-h1); h1++; } else { t=t(v1+g1); g1++; u=u(v-h); h++; } } ans1=(udiff[i][j]/fact(j+1)); ans2=(tdiff[z][j]/fact(j+1)); ans=ans+(ans1+ans2)/2; if(j%2==0) i--; else z--;} printf("\n\n the value of y when x=%f is y=%f",x0,ans); getch();
//Write a program to implement Newton Gregory forward interpolation formula #include<stdio.h> #include<conio.h> #include<math.h> void main() { int i,j,n; float xy[10][11],h,p,px=1,x,y; char str[80]; clrscr(); printf("Enter the number of data : "); scanf("%d",&n); printf("\nEnter the data : \n"); for(i=0;i<n;i++) { printf("x(%d) and y(%d) : ",i+1,i+1); scanf("%f%f",&xy[i][0],&xy[i][1]); } for(j=2;j<n+1;j++) for(i=0;j<n-1;j++) xy[i][j]=xy[i+1][j-1]-xy[i][j-1]; printf("\nThe diference table is :- "); printf("\nx f(x) "); for(i=0;i<n-1;i++) printf("?^%d ",i+1); for(i=0;i<n;i++) { printf("\n"); for(j=0;j<n+1-i;j++) { printf("%.4f ",xy[i][j]); } } printf("\nEnter the value of 'x' : "); scanf("%f",&x); h=xy[i][0]-xy[0][0]; p=(x-xy[0][0])/h; y=xy[0][1]; for(i=1;i<n;i++) { px=(p-(i-1))/i; y+=xy[0][i+1]px; } printf("\n The value of function at x =%f is %f ",x,y); getch();
//Write a program to implement gauss forward interpolation formula #include<stdio.h> #include<conio.h> #include<math.h> void main() { int i,j,n; float ax[10],ay[10],xy[20][20],diff[20][20]; float y1,y2,y3,y4,x,y=0,h,p,nr,dr; clrscr(); printf("\nEnter the number of terms : "); scanf("%d",&n); printf("\nEnter the value in the form of x and y :- \n"); for(i=0;i<n;i++) { printf("Enter the value of x%d and y%d :- ",i,i); scanf("%f %f ",&ax[i],&ay[i]); } printf("\nEnter the value of x for which you want value of y :- "); scanf("%f",&x); h=ax[1]-ax[0]; for(i=0;i<n-1;i++) { xy[i][0]=ax[i]; xy[i][0]=ay[i]; } for(i=0;i<n-1;i++) { diff[i][1]=ay[i+1]-ay[i]; } for(j=2;j<=4;j++) { for(i=0;i<n-j;i++) { diff[i][j]=diff[i+1][j-1]-diff[i][j-1]; } } for(j=2;j<=n+1;j++) for(i=0;i<=n-1;i++) xy[i][j]=xy[i+1][j-1]-xy[i][j-1]; printf("The difference table is :- "); printf("\nx f(x) "); for(i=0;i<n-1;i++) printf("^%d :",i+1); for(i=0;i<n;i++) { printf("\n"); for(j=0;j<n+1-i;j++); printf("%.4f",xy[i][j]); } i=0; do {
i++;} while(ax[i]<x); i--; p=(x-ax[i])/h; y1=pdiff[i][1]; y2=p(p-1)diff[i-1][2]/2; y3=(p+1)p(p-1)diff[i-2][3]/6; y4=(p+1)p(p-1)(p-2)diff[i-3][4]/24; y=ay[i]+y1+y2+y3+y4; printf("\n When x = %6.4f,y = %6.8f",x,y); printf("\n\n\n press enter to exit"); getch();
