Math Preperation Zone: Program Codes and Algorithms

1. Bisection method-[You must be registered and logged in to see this link.]/FlowChart
   
2. False position method-Program/FlowChart
   
3. Newton-Raphson Methhod-[You must be registered and logged in to see this link.]/FlowChart
   
4. Secant Method-[You must be registered and logged in to see this link.]/FlowChart
   
5. Fixed-Point Method-[You must be registered and logged in to see this link.]/FlowChart
   

1. Jacobi Iteration Method-[You must be registered and logged in to see this link.]/Flow Chart
   
2. Gauss-Seidel Method-Program/FlowChart
   
3. Method of Relaxation-Program/FlowChart
   

1. Trapezoidal Rule-Program/FlowChart/[You must be registered and logged in to see this link.]
   
2. Simpson't Rule-Program/FlowChart
   

Links will be upgraded depending on YOUR contributions

(note: I think all of us know the program codes of Chapter 6, still if you need it, I can post. Give more priorities to Flow Charts)

Code:


#include<math.h>
#include<iostream>
#include<stdio.h>
#define EPS 0.000001
#define maxit 100
using namespace std;

void jacobi(int n, float a[10][10], float b [10], float x[10], int *count, int *status )
        {
            int i,j,key;
            float sum, x0[10];

            for(i=1; i<=n; i++)
                x0[i]= b[i] / a[i][i];
            *count = 1;
            begin:
            key = 0;
            for(i=1; i<=n; i++)
                {
                    sum = b[i];
                    for(j=1;j<=n;j++)
                        {
                            if(i==j)continue;
                            sum = sum - a[i][j] * x0[j];
                        }
                    x[i] = sum / a[i][j];
                    if(key==0)
                        {
                            if(fabs((x[i]- x0[i])/x[i])> EPS)
                                key = 1;
                        }
                }
                if(key == 1)
                    {
                        if(*count == maxit)
                            {
                                *status = 2;
                                return;
                            }
                        else
                            {
                                *status = 1;
                                for(i=1;i<=n;i++)
                                    x0[i]= x[i];

                            }
                        count = count +1 ;
                        goto begin;
                    }
        return;
        }

int main(){
    int i,j,n,count,status;
    float a[10][10], b[10], x[10];

    printf("\n Solution by Jacobi iteration\n");
    printf("\n What is the size n  of the system?\n ");
    scanf("%d", &n);
    printf("\nInput coefficient a(i,j), row by row \n");
    for(i=1;i<=n;i++)
        for(j=i;j<=n;j++)
            scanf("%f", &a[i][j]);
    printf("\nInput vector b\n");
    for(i=1;i<=n;i++)
        scanf("%f",&b[i]);
    jacobi(n, a, b, x, &count, &status);

    if(status==2)
        {
        printf("\n No converence in %d  itrerations\n\n", maxit);

        }
    else
        {
            printf("\n\tSelection vector x \n\n");
            for(i=1;i<=n;i++)
                printf("%15.6f",x[i]);
            printf("\n\n Iterations = %d", count);

        }

    return 0;
    }



Code:


#include<math.h>
#include<iostream>
#include<stdio.h>
#define EPS 0.000001
#define maxit 50
using namespace std;

void gaseid(int n, float a[10][10], float b [10], float x[10], int *count, int *status )
        {
            int i,j,key;
            float sum, x0[10];

            for(i=1; i<=n; i++)
                x0[i]= b[i] / a[i][i];
            *count = 1;
            begin:
            key = 0;
            for(i=1; i<=n; i++)
                {
                    sum = b[i];
                    for(j=1;j<=n;j++)
                        {
                            if(i==j)continue;
                            sum = sum - a[i][j] * x0[j];
                        }
                    x[i] = sum / a[i][j];
                    if(key==0)
                        {
                            if(fabs((x[i]- x0[i])/x[i])> EPS)
                                key = 1;
                        }
                }
                if(key == 1)
                    {
                        if(*count == maxit)
                            {
                                *status = 2;
                                return;
                            }
                        else
                            {
                                *status = 1;
                                for(i=1;i<=n;i++)
                                    x0[i]= x[i];

                            }
                        count = count +1 ;
                        goto begin;
                    }
        return;
        }

int main(){
    int i,j,n,count,status;
    float a[10][10], b[10], x[10];

    printf("\n Solution by Gauss-Shidel iteration\n");
    printf("\n What is the size n  of the system?\n ");
    scanf("%d", &n);
    printf("\nInput coefficient a(i,j), row by row \n");
    printf("\n One row Each line\n");
    for(i=1;i<=n;i++)
        for(j=i;j<=n;j++)
            scanf("%f", &a[i][j]);
    printf("\nInput vector b\n");
    for(i=1;i<=n;i++)
        scanf("%f",&b[i]);
    gaseid(n, a, b, x, &count, &status);

    if(status==2)
        {
        printf("\n No converence in %d  itrerations\n\n", maxit);

        }
    else
        {
            printf("\n\tSelection vector x \n\n");
            for(i=1;i<=n;i++)
                printf("%15.6f",x[i]);
            printf("\n\n Iterations = %d", count);

        }

    return 0;
    }




Code:


[code]The C codes here[/code]


Code:

#include <stdio.h>

so you need to write like this:

Code:


[code]
#include<stdio.h>
//what  ever codes you have here
int main(void){
return 0;
}
[/code]


See?
easy, eh?

Can you please do it Saiful? Or else, we will have programs which are like:
#include
#include
#include

Code:




/*Secant Method for determining the root of non linear equations*/
/*By Amit*/
/*Algorithm method from Numerical Methods by E.Balaguruswamy*/

#include<stdio.h>
#include<math.h>
#define Err 0.000001
#define MAXIT 50
#define F(x) (x)*(x)+(x)-2

int main(void)
{
 int counter=1;
 int con = 1; 
 int flag = 0;
 float x1, x2, x3, root=0;
 float f1, f2=0;
 
 printf("Enter your x1: "); 
 scanf("%f",&x1);

 
 printf("\nEnter your x2: "); 
 scanf("%f",&x2);
 
 f1 = F(x1);
 f2 = F(x2);
 
 
 while (con)
 {
  if((fabs(f1-f2))<Err)
  {
  printf("Error: Division by zero\n");
  con = 0;
  break;
  }
  x3 = (((f2*x1)-(f1*x2))/(f2-f1));
  if(fabs((x3-x2)/(x3))>Err)
  {
  if(counter==MAXIT ){
    printf("\nError: no convergence in %d iterations\n",MAXIT);
    con=0;
    break;
  }
  x1=x2;
  f1=f2;
  x2=x3;
  f2=F(x3);
  counter ++;
  }
  else
  {
  con=0;
  root = x3;
  flag = 1;
  break;
  }
 }
 if(flag)
 {
  printf("\nroot is %f",root);
  printf("\nFunction value at root is %f",F(root));
  printf("\nNUmber of iterations %d\n",counter);
 }
 return 0;
}




Code:



/*Newton RaphSon Method for determining the root of non linear equations*/
/*By Amit*/
/*Algorithm method from Numerical Methods by E.Balaguruswamy*/


#include<stdio.h>
#include<math.h>
#define Err 0.000001
#define F(x) (x)*(x)+(x)-2
#define DF(x) 2*(x)+1
#define MAXIT 100

int main(void)
{
 int counter=1;
 int con = 1; 
 float x0, x1=0;
 float fx;
 float xn;
 float fdx;

 printf("Enter your value of X: ");
 scanf("%f",&x0) ;
 printf("\n");
 while (con)
 {

  fx=F(x0);
  fdx=DF(x0);
  xn=x0-(fx/fdx);
  if(fabs((xn-x0)/xn)<Err)
  {
  printf("\nThe root is %f",xn);
  printf("\nThe value of function using root is %f",F(xn));
  printf("\nThe number of iterations to reach root is %d\n",counter);
 
  con = 0;
  }
  else
  {
  x0=xn;
  counter++;
  if(counter>MAXIT)
  {
    printf("\nThe solution does not converge in\n");
    con=0;
 
  }
 
  }
 
 }
 return 0;
}


Code:



/*
Fixed Point Method for determining the roots of non linear equations
By Amit
Algorithm method from Numerical Methods by E.Balaguruswamy
*/

#include <stdio.h>
#include <math.h>

#define Err 0.000001
#define F(x) (x)*(x)+(x)-2

int main(void){
 float x0, x1, x2, root, f0, f1, f2=0;
 int counter=0;
 int con;
 
 printf("Enter your x1: "); 
 scanf("%f",&x1);

 
 printf("\nEnter your x2: "); 
 scanf("%f",&x2);

 f1=F(x1);
 f2=F(x2);
 if((f1*f2)>0)
 {
  printf("Does not brace root \n");
  counter++;
  return 0;
 }

 while(con)
 {
  counter=counter +1 ;
  //counter++;
 
  x0=x1-f1*(x2-x1)/(f2-f1);
 
  f0=F(x0);
 
  if(f1*f0<0)
  {
  x2=x0;
  f2=f0;
  }
  else
  {
  x1=x0;
  f1=f0;
  }
  printf("%f \t %f\n",x1,x2);
  if(fabs((x1-x2)/x2) < Err)
  {
    root = (x1+x2)/2;
   
    con=0;
  }
 }
 printf("The root is %e\n",root);
 printf("the number of iteration is %d\n",counter);
 printf("The value of F(root) is %f\n", F(root));

 return 0;
}




Code:




#include <stdio.h>
#include <math.h>
#define EPS  0.000001
#define F(x)  ((x)*(x))+(x)-2
int main(){

 float x1, x2, x0=0.0;
 float f1=0.0;
 float f2=0.0;
 float f0=0.0;
 float root=0.0;
 int counter =0;
 int con=1;
 
 printf("Enter your x1: "); 
 scanf("%f",&x1);

 
 printf("\nEnter your x2: "); 
 scanf("%f",&x2);

 f1=F(x1);
 f2=F(x2);
 printf("\nthe value of F1 is %f",f1);
 printf("\nthe value of F2 is %f",f2);

 if ((f1*f2)>0)
 {
  printf("\nThe values do not brace any roots\nProgram exiting.");
  return 0;
 }
 else
 {
  while (con)
  { counter ++;
  x0=((x1+x2)/2);
  printf("\nx0 = %f",x0);
  f0=F(x0);
  printf("\tf0 = %f",f0);
  //please look at this part carefully. this part is absent in Book's algorithm
  if(f0==0){
  root = x0;
  break;
  }
  if ((f1*f0)<0)
  {
    x2=x0;
       
  }else
  {
    x1=x0;
    f1=f0;
  }
  if(fabs((x1-x2)/x2) < EPS)
  {
    root = (x1+x2)/2;
   
    con=0;
  }
  }
 }
  printf("\nThe value of the root is : %e\n",root);
  printf("\nthe value of the function using the root is %e\n",F(root));
  printf("\nthe value of the counter is %d\n",counter);
 return 0;
}





Code:


#include<stdio.h>

#include<conio.h>

#include<math.h>



int main(void){

   int n = 3, key, i, j;

   double a[3][3] = {

   2, 1, 1,

   3, 5, 2,

   2, 1, 4

   };

   int b[3] = {5, 15, 8};

   double x0[3], x[3], sum;

   clrscr();



   for(i=0; i<n; i++)

      x0[i] = b[i]/a[i][i];



   again:

   key = 0;



   for(i=0; i<n; i++){

      sum = b[i];

      for(j=0; j<n; j++){

         if(i!=j)

            sum -= (a[i][j]*x0[j]);

      }

      x[i] = sum/a[i][i];

      if(fabs((x[i]-x0[i]))>.0000001)

         key = 1;

      if(key==1){

         x0[i] = x[i];

         goto again;

      }

   }



   for(i=0; i<n; i++)

      printf("%f\n", x[i]);



   getch();

   return 0;

}


Code:


/*Simple Trapezoid Rule for determining the integration of formula*/
/*By Amit*/
/*Algorithm method from Numerical Methods by E.Balaguruswamy*/
/*
======special note for gcc users==========
use an -lm switch to compile this program correctly as the switch  manually links the exp function used here.
for example:
gcc trapezoid.c -lm
*/


#include<stdio.h>
#include<math.h>


float F(float x){
    float f ;

    f = 1.0-(exp(-x/2.0));

    return f;
}
int main(void){
    int n,i;
    float a,b,h,c,sum,ict;
    printf("give intial value of x: ");
    scanf("%f",&a);
    printf("\ngive the final value of x: ");
    scanf("%f",&b);
    printf("\nenter the segmentation width: ");
    scanf("%f",&h);
    n=(b-a)/h;
    sum = ( F(a) + F(b) )/2.0;
    for(i=1;i<=n-1;i++){
        sum = sum + F(a+i*h);
    }
    ict = sum*h;
    printf("\n");
    printf("the integration between %f and %f ",a,b);
    printf("\nwhere h=%e is %f\n",h,ict);
    printf("\n");
}


BIT0107-toma wrote:@Amit::::
[You must be registered and logged in to see this image.] oita amii delete korchi..not u.. [You must be registered and logged in to see this image.]

bhai, code gula ektu uplaod kor
@AMIT............apni doya kore nijer kora kisu jinish o upload koiren
kebol onner ta na

Spoiler: