ALGORITHM OF TRAPEZOIDAL RULE

ALGORITHM OF TRAPEZOIDAL RULE

1-Enter value of lower limit (a) & upper limit (b)

2-Enter the no. of sub-intervals (n)

3-h = (b-a) / n

4- s = y(a) + y(b)

5- for (j=1 to n-1)

  {

   s = s+2*y(a+i*h)

   }

6-Result = (h/2) * s

7- Print result

8- Exit ( )

ALGORITHM OF SIMPSON 3/8 RULE

ALGORITHM OF SIMPSON 3/8 RULE

1-Enter value of upper limit (a) and lower limit(b)

2-Enter value of sub-interval (n)

3-h = (b-a) / n

4-s = y(a) +y(b)

5-for (j = 1 to n-1)

   if (j % 3 = = 0)

   s = s+2*y(a+j*h)

   else

   s= s +3*y(a+j*h)

6- result = 3*(h/8) * s

7-Print result

8-exit ( )

ALGORITHM OF SIMPSON’S 1/3 RULE

ALGORITHM OF SIMPSON’S 1/3 RULE

1-Enter value of upper limit & lower limit

2-Enter value of sub-interval(n)

3-h=(b-a)/n

4-s=y(a)+y(b)

5-For (j=1 to n-1) dø

   if( j%2==0)

  {

   s= s+2*y(a+j*h)

  else

  s=s+4*y(a+j*h)
  }

6-Result = (h/3)*s

7-Print  “result”

8- exit( )

ALGORITHM FOR REGULA FALSI

ALGORITHM FOR  REGULA FALSI

1. Input the values of x0,x1,e,n.where e is the error allowed and n  is the maximum number of iteration.

2. Find f(x0)*f(x1) and if [f(x0)*f(x1)]<0

   {

3.    for (i=1 to n)

   }

    4. calculate x2=[x0f(x1)-x1f(x0)]/f(x0)-f(x1)

    5. if |f(x2)|<e and if [f(x0)*f(x2)<0]

        x1=x2

    6. else

       x0=x2

    7. print (“Root is x2”)

ALGORITHM FOR NEWTON RAPHSON METHOD

ALGORITHM FOR NEWTON RAPHSON METHOD

1.    Start
2.    Read the values of x0,e,delta,n;

   Where x0 is initial approximation, e is error      

   allowed. delta is the slope and n is

   maximum number of iteration.

 

3.    for i=1 to n,
4.    if | f(x0 )|<delta,

   then goto 9

5.    x1= x0 –[f (x0  )/f (x0 )]
6.    if |( x0 – x1)/ x0 | <e, then goto 11
7.    write “Solution does not converge in n

          iteration”.

8.    Stop
9.    Write “Slope is too small”.
10. Stop
11. Write ”Convergent solution is x”.
12. Stop

ALGORITHM FOR BISECTION METHOD

ALGORITHM FOR BISECTION METHOD

1- Enter f(x), error, max_iteration.

2- Enter a and b such that f (a).f (b) <0.

3- if f (a).f (b)>0 then

                             goto step 2

4- for (i=0; i<max_iteration; i++)

     {

       x= (a+b)/2

           if f(x).f (a) <0

                  b=x;

           else

                   a=x;

            if [(b-a)/b <=error]

            {

               printf “Root is x”

               Stop

             }

      }

5- printf “Solution does not converge in  

   max_iteration.

6- Stop