Straight Line Fit Using Least Squares Estimate

 #include<stdio.h>  
 #include<math.h>  
   
 void main()  
 {  
       float x[100],y[100],xy[100],xsquare[100],m,sumx,sumy,sumxy,sumxsq,a,b;  
         
       int i,j,k;  
   
   
       sumx=sumy=sumxy=sumxsq=0;  
       printf("\n\t\t\tLeast Square Method To Fit A Staright Line");  
       printf("\n=========================================================================================================================\n");  
       printf("\t\t\tEnter the value of m(number of terms) ");  
       scanf("%f",&m);  
       printf("\n=========================================================================================================================\n");  
       printf("\t\t\tEnter all the value of X \n");  
       for(i=0;i<m;i++)  
       {  
             printf("\tx[%d]=",i);  
             scanf("%f",&x[i]);  
             xsquare[i]=x[i]*x[i];//xsquare being calculated here  
             sumx=sumx+x[i];//summation of x  
             sumxsq=sumxsq+xsquare[i];//summation of x square calculated  
       }  
       printf("\n=========================================================================================================================\n");  
       printf("\t\t\tEnter all the value of Y \n");  
       for(i=0;i<m;i++)  
       {  
             printf("\ty[%d]=",i);  
             scanf("%f",&y[i]);  
             xy[i]=x[i]*y[i];//x*y being calculated  
             sumy=sumy+y[i];// summation of Y calculated  
             sumxy=sumxy+xy[i];//summation of XY calculated  
       }  
       a=((sumy*sumxsq)-(sumx*sumxy))/((m*sumxsq)-(sumx*sumx));  
       b=((m*sumxy)-(sumx*sumy))/((m*sumxsq)-(sumx*sumx));  
       printf("\n=========================================================================================================================\n\n");  
         
       printf("\t\t\tValue of a=%4.3f\tvalue of b=%4.3f\n",a,b);  
         
       printf("\n\t\t\tThus equation will be y=%4.3f + %4.3fx\n\n",a,b);  
         
       getchar();  
 }  
   

Fourth Order Runge-Kutta Method For Differential Equation

 #include<stdio.h>  
 #include<math.h>  
 float funct(float,float);  
 void main()  
 {  
      float y0,yprime,k1,k2,k3,k4;  
      float h,x,iter,x0;  
      printf("\n\t\t\tFourth Order Runge-Kutta Method To Solve Differential Equation");  
      printf("\n=========================================================================================================================\n");  
      printf("\t\t\tEnter the value of h(the interval) ");  
      scanf("%f",&h);  
      printf("\n=========================================================================================================================\n");  
      printf("\t\t\tEnter the value of X(for which you need value of y) ");  
      scanf("%f",&x);  
      printf("\n=========================================================================================================================\n");  
      printf("\t\t\tEnter the intital value y0 ");  
      scanf("%f",&y0);  
      printf("\n=========================================================================================================================\n");  
      printf("\t\t\tEnter the intital value x0 ");  
      scanf("%f",&x0);  
      for(iter=x0;iter<=x;iter=iter + h)  
      {  
           k1=funct(iter,y0);  
           k2=funct(iter+(h/2),y0+(k1*h)/2);  
           k3=funct(iter+((h/2)),y0+(k2*h)/2);  
           k4=funct(iter+h,y0+(k3*h));  
           yprime=y0+((h/6)*(k1+2*(k2+k3)+k4));  
           printf("\n\tValue of X=%f then Value of Y=%f ",iter,y0);  
           y0=yprime;  
      }  
      getchar();  
 }  
 float funct(float x,float y)  
 {  
      return ((x-y)/(x+y));  
 }  

Euler's Method For Numerical Differentiation

 #include<stdio.h>  
 #include<math.h>  
 float funct(float,float);  
 void main()  
 {  
      float y0,yprime;  
      float h,x,iter,x0;  
      printf("\n\t\t\tEuler's Method To Solve Differential Equation");  
      printf("\n=================================================================================================================\n");  
      printf("\t\t\tEnter the value of h(the interval) ");  
      scanf("%f",&h);  
      printf("\n=================================================================================================================\n");  
      printf("\t\t\tEnter the value of X(for which you need value of y) ");  
      scanf("%f",&x);  
      printf("\n=================================================================================================================\n");  
      printf("\t\t\tEnter the intital value y0 ");  
      scanf("%f",&y0);  
      printf("\n=================================================================================================================\n");  
      printf("\t\t\tEnter the intital value x0 ");  
      scanf("%f",&x0);  
      for(iter=x0;iter<=x;iter=iter + h)  
      {  
           yprime=y0+(h*funct(iter,y0));  
           printf("\nWhen X=%f then Y=%f",iter,y0);  
           y0=yprime;  
      }  
      getchar();  
 }  
 float funct(float x,float y)  
 {  
      return ((x-y)/(x+y));  
 }  

Simpson's 3/8th Rule

 #include<stdio.h>  
 float integrate(float);  
 void main()  
 {  
      float a,b,h,n,sum=0;  
      int i;  
      printf("\n\tINTEGRATION THROUGH SIMPSON' 3/8 RULE");  
      printf("\n\t====================================");  
      printf("\n\nEnter the upper limit a ");  
      scanf("%f",&a);  
      printf("\n\nEnter the lower limit b ");  
      scanf("%f",&b);  
      printf("\n\nEnter the number of sub-intervals ");  
      scanf("%f",&n);  
      h=(b-a)/n;  
      sum=integrate(a)+integrate(b);  
      for(i=1;i<n;i++)  
      {  
           if(i%3==0)  
                sum=sum+(2*integrate(a+i*h));  
           else  
                sum=sum+(3*integrate(a+i*h));  
      }  
      sum=sum*((3*h)/8);  
      printf("\nThe value of integral is %f",sum);  
 }  
 float integrate(float n)  
 {  
      return 1/(1+(n*n));  
 }  

Simpson's 1/3rd Rule

 #include<stdio.h>  
 float integrate(float);  
 void main()  
 {  
      float a,b,h,n,sum=0;  
      int i;  
      printf("\n\tINTEGRATION THROUGH SIMPSON' 1/3 RULE");  
      printf("\n\t====================================");  
      printf("\n\nEnter the upper limit a ");  
      scanf("%f",&a);  
      printf("\n\nEnter the lower limit b ");  
      scanf("%f",&b);  
      printf("\n\nEnter the number of sub-intervals ");  
      scanf("%f",&n);  
      h=(b-a)/n;  
      sum=integrate(a)+integrate(b);  
      for(i=1;i<n;i++)  
      {  
           if(i%2==0)  
                sum=sum+(2*integrate(a+i*h));  
           else  
                sum=sum+(4*integrate(a+i*h));  
      }  
      sum=sum*(h/3);  
      printf("\nThe value of integral is %f",sum);  
 }  
 float integrate(float n)  
 {  
      return 1/(1+(n*n));  
 }  

Trapezoidal Method Of Numerical Integration

 #include<stdio.h>  
 float integrate(float);  
 void main()  
 {  
      float a,b,h,n,i,sum=0;  
      printf("\n\tINTEGRATION THROUGH TRAPEZOIDAL RULE");  
      printf("\n\t====================================");  
      printf("\n\nEnter the upper limit a ");  
      scanf("%f",&a);  
      printf("\n\nEnter the lower limit b ");  
      scanf("%f",&b);  
      printf("\n\nEnter the number of sub-intervals ");  
      scanf("%f",&n);  
      h=(b-a)/n;  
      sum=integrate(a)+integrate(b);  
      for(i=1;i<n;i++)  
           sum=sum+(2*integrate(a+i));  
      sum=sum*(h/2);  
      printf("\nThe value of integral is %f",sum);  
 }  
 float integrate(float n)  
 {  
      return 1/(1+(n*n));  
 }  

Lagrange's Interpolation Formula

 #include<stdio.h>  
 #include<math.h>  
 void main()  
 {  
      float ax[10],y[10];  
      float x,numsum=1,densum=1,k;  
      int i,j,n;  
      printf("Enter the number of terms ");  
      scanf("%d",&n);  
      printf("\n=======================================================\n");  
      printf("Enter the array ax ");  
      for(i=0;i<n;i++)  
      {  
           printf("\nEnter the value of ax[%d] = ",i);  
           scanf("%f",&ax[i]);  
      }  
      printf("\n=======================================================\n");  
      for(i=0;i<n;i++)  
      {  
           printf("Enter the value of y[%d] = ",i);  
           scanf("%f",&y[i]);  
      }  
      printf("\nEnter the interpolation point ");  
      scanf("%f",&x);  
      k=0;  
      for(i=0;i<n;i++)  
      {  
           numsum=1;  
           densum=1;  
           for(j=0;j<n;j++)  
           {  
                if(i!=j)  
                {  
                     numsum=numsum*(x-ax[j]);  
                     densum=densum*(ax[i]-ax[j]);  
                }  
           }  
           k=k+(numsum/densum)*y[i];  
      }  
      printf("\nValue at %f is %f ",x,k);  
      getchar();  
 }