programming language codes

/*Gauss Elimination */ # include <stdio.h> # include <conio.h> # include <math.h> # define MAX 10 void main() { int i,j,n,k; float mat[MAX][MAX],x[MAX],temp,pivot,sum=0; clrscr(); printf("\t\t\t GAUSS ELIMINITION METHOD\n"); printf("-------------------------------------------------------------------\n"); printf("Enter No of Equtions : "); scanf("%d",&n); printf("Enter Coefficients of Eqution \n"); for(i=1;i<=n;i++) for(j=1;j<=n;j++) scanf("%f",&mat[i][j]); printf("Enter Constant value\n"); for(i=1;i<=n;i++) { scanf("%f",&mat[i][n+1]); x[i]=mat[i][n+1]; } for(i=2;i<=n;i++) { for(j=i;j<=n;j++) { pivot=mat[j][i-1]/mat[i-1][i-1]; for(k=i-1;k<=n+1;k++) mat[j][k]=mat[j][k]-pivot*mat[i-1][k]; } } printf("Eliminated matrix as :- \n"); for(i=1;i<=n;i++) { for(j=1;j<=n+1;j++) printf("\t%.2f",mat[i][j]); p...

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/*Trapezoidal rule */ # include <stdio.h> # include <conio.h> # define MAX 20 void main() { int i,j,n; float x[MAX],y[MAX],sum=0,h,res; clrscr(); printf("Solution using Trapezoidal rule \n"); printf("Enter Number of data points : "); scanf("%d",&n); printf("Enter value of table value set by set\n"); for(i=1;i<=n;i++) { printf("Enter value of x[%d] and y[%d] ",i,i); scanf("%f%f",&x[i],&y[i]); } h=x[2]-x[1]; printf("\nInterval :=%f\n",h); sum=y[1]+y[n]; for(i=2;i<n;i++) sum=sum+y[i]*2; res=sum*(h/2); printf ("Integral from %3.2f to %3.2f is : = %f",x[1],x[n],res); getch(); } OUTPUT :- Solution using Trapezoidal rule Enter Number of data points : 6 Enter value of table value set by set Enter value of x[1] and y[1] 7.47 1.93 Enter value of x[2] and y[2] 7.48 1.95 Enter value of x[3] and y[3] 7.49 1.98 Enter value of x[4] and y[4] 7.50 2.01 Ente...

/*Simpson 1/3 Rule */ # include <stdio.h> # include <conio.h> # define MAX 20 void main() { int i,j,n; float x[MAX],y[MAX],sum=0,h,res; clrscr(); printf("Solution of 1/(1+x)dx using Simpson's 1/3 rule \n"); printf("Enter Number of data points : "); scanf("%d",&n); printf("Enter value of table value set by set\n"); for(i=1;i<=n;i++) { scanf("%f",&x[i]); y[i]=1/(x[i]+1); } printf("X \t\t Y\n"); for(i=1;i<=n;i++) printf("%f\t%f\n",x[i],y[i]); h=x[2]-x[1]; printf("\nSegment Interval `h':=0.25\n"); sum=sum+y[1]+y[n]; for(i=2;i<n;i++) { if(i%2==0) sum=sum+y[i]*4; else sum=sum+y[i]*2; } res=sum*(0.25/3); printf ("Integral from %3.2f to %3.2f is : = %f",x[1],x[n],res); getch(); } OUTPUT Solution of 1/(1+x)dx using Simpson's 1/3 rule Enter Number of data points : 5 Enter value of table value for x column 0 .25 .50 .75 1 X Y ...

/*Simpson 3/8 rule */ # include <stdio.h> # include <conio.h> # define MAX 20 void main() { int j,n=0; float x[MAX],y[MAX],sum=0,h,res,lb,ub,i; clrscr(); printf("Solution of 1/(1+x)dx using Simpson's 3/8 rule \n"); printf ("Enter initial value : "); scanf("%f",&lb); printf("Enter final value : "); scanf("%f",&ub); printf("Enter no. of Subinterval : "); scanf("%f",&h); h=(ub-lb)/h; for(i=lb;i<=ub;i=i+h) { x[n]=i; y[n]=1/(1+x[n]); n++; } printf("No.\t X\t\tY=1/(1+x)\n"); printf("---------------------------------------\n"); sum=y[0]+y[n-1]; for(j=0;j<n;j++) printf("%d\t%f\t%f\n",j,x[j],y[j]); printf("---------------------------------------\n"); for(j=1;j<n-1;j++) { if(j%3==0) sum=sum+y[j]*2; else sum=sum+y[j]*3; } res=((3*h)/8)*sum; printf("\nIntegral from %f to %f when h = %f is = %f",x[0],x[n-1...

/* Runge-kutta method of 4th order to solve 10*dy/dx=(x*x)+(y*y)*/ # include <stdio.h> # include <conio.h> void main() { int c=0; float x,y0,xp,h,i,y1,m1,m2,m3,m4; float f(float,float); clrscr(); printf("Solution by Runge kutta 2nd order Method\n"); printf("Enter initial Boundry condition x,y : "); scanf("%f%f",&x,&y0); printf("Enter Value of X at which Y is required : "); scanf("%f",&xp); printf("Enter Interval ,h : "); scanf("%f",&h); printf(" No. X\t m1 \t m2\t m3 \t m4 \t Y\n"); printf("-------------------------------------------------------------------\n"); for(i=x;i<=xp;i=i+h) { c++; m1=h*f(i,y0); m2=h*f(i+(h/2),y0+(m1/2)); m3=h*f(i+(h/2),y0+(m2/2)); m4=h*f(i+h,y0+m3); y1=y0+((m1+2*m2+2*m3+m4)/6); printf("%2d %5.6f %5.6f %5.6f %5.6f %5.6f %5.6f\n",c,i,m1,m2,m3,m4,y1); y0=y1; } getch(); } ...