Numerical Methods Practical Flle_MDU

7/27/2019 Numerical Methods Practical Flle_MDU

1/29Department of Electronics & Communication Engineering, YCET, Narnaul, Haryana

NNAARRNNAAUULL ((HHAARRYYAANNAA))

PRACTICAL FILE

OF

Numerical Methods

USING C LAB

Submitted in Partial Fullfillment of the Requirment in

Electronics & Communication Engineering

(Session 2012-2015)

Submitted to : Submitted by:

Mr. Yogesh Gupta Subhash Kumar Yadav

( Lectt. ) ECE 4th

Sem.

Roll No:12ECEL26



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((HH

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CCEERRTTIIFFIICCAATTEE

This to certify that Subhash Kumar Yadav has completed her practical lab file of NUMERICAL

METHODS OF COMPUTATIONAL PROGRAMMING LAB under my guidance and completed it to

my total satisfaction submitted in partial fullfillment of the requirment in

EElleeccttrroonniiccss &&CCoommmmuunniiccaattiioonn EEnnggiinneeeerriinngg

(Session 2012-2015)

Submitted to : Submitted by:

Mr. Yogesh Gupta Subhash Kumar Yadav

( Lectt. ) ECE 4th

Sem.

Roll No:12ECEL26



NUMERICAL METHODS LAB.

INDEX

Sr.NO Program Name Page No. Date Lect. Sign

1.Program to implement Bisection method to findthe root of given equation. 1-2

2.

Program to implement Newton-Rapson method to

find root of given equation.

3-4

3.

Program to find solution of system of linear

equation using Gauss elimination technique with

pivoting.

5-7

4.


equation using Gauss-Jordon technique. 8-9

5.


equation using Gauss-Seidel method. 10-12

6.

Program to find the largest Eigen value using

Power method.

13-15

7.

Program to fit a polynomial of degree m through

a set of points using method of least squares.

16-19

8.

Program to implement Trapezoidal rule for

tabulated function.

20

9.

Program to implement Simpsons 1/3 rule for

tabulated function.

21-22

10.

Program to solve ODE of type dy/dx=xy using

Eulers method.

23-24

11.

Program to solve ODE of type dy/dx=xy usingsecond order Runge-Kutta method(Heuns

method)

25-26



Program No: 1

Aim: Program to implement Bisection method to find the root of given

equation.

#include

#include

#include

#include

double f(double x)

{

return pow((double)x,(double)3.0)-4*x-9;

}

void main()

{

float x1,x2,epsilon,x3;

clrscr();

printf("Enter first point of the search interval:");

scanf("%f",&x1);

printf("Enter second point of the search interval:");

scanf("%f",&x2);

if((f(x1)*f(x2))>0)

{

printf("\n Initial approximations are unsuitable\n");

exit(1);

}

printf("Enter prescribed tolerance:");scanf("%f",&epsilon);

do

{

x3=(x1+x2)/2;

if(f(x1)*f(x3)



}

while( fabs((double)(x1-x2)) > epsilon);

printf("\nApproximate root=%8.4f\n",x3);

getch();

}

Output:

Enter first point of the search interval:2

Enter second point of the search interval:3

Enter prescribed tolerance:.001

Approximate root= 2.7061



Program No: 2

Aim: Program to implement Newton-Rapson method to find root of given

equation.

#include

#include

#include

#include

double f(double x)

{

return x*x*x-4.0*x-9.0;

}

double df(double x)

{

return 3.0*x*x-4.0;

}

void main()

{

float x0,x1,epsilon,delta,relativeerror;int i,n;

clrscr();

printf("Enter initial approximation:");

scanf("%f",&x0);

printf("Enter number of iterations permitted:");

scanf("%d",&n);

printf("Enter prescribed tolerance:");

scanf("%f",epsilon);

printf("Enter lower bound on slope:");

scanf("%f",&delta);

for(i=1;i



}

x1=x0-f(x0)/df(x0);

relativeerror=fabs((x1-x0)/x1);

x0=x1;

if (relativeerror



Program No: 3

Aim: Program to find solution of system of linear equation using Gauss

elimination technique with pivoting.

#include

#include

#include

#define MAX 20

void main()

{

float a[MAX][MAX],x[MAX],max,temp,sum;int i,j,k,m,n,p,q;

clrscr();

printf("Enter number of equations:");

scanf("%d",&n);

printf("\nEnter coefficients equation wise\n");

for(i=1;i



if(p!=k)

{

for(q=k;q



Output:

Enter number of equations:2

Enter coefficients equation wise

3

2

5

8

6

9

Required solution is

x(1)=56403.301

x(2)=-6.500



Program No: 4

Aim: Program to find solution of system of linear equation using Gauss-

Jordon technique

#include

#include

#include

#define MAX 20

void main()

{

float a[MAX][MAX],temp,comm;

int i,j,k,m,n,p,q;

clrscr();


scanf("%d",&n);


for(i=1;i



a[i][j]=a[i][j]-comm*a[k][j];

}

}

}

printf("\n\nRequired solution is\n");

for(i=1;i



Program No: 5

Aim: Program to find solution of system of linear equation using Gauss-Seidel

method.

#include

#include

#include

#define MAX 20

void main(){

float a[MAX][MAX],x[MAX],max,temp,sum;

int i,j,k,m,n,p,q;

clrscr();


scanf("%d",&n);


for(i=1;i



}

}

if(p!=k)

{

for(q=k;q



Output:

Enter number of equations:2

Enter coefficients equation wise

4

9

6

7

8

2

Required solution is

x(1)=56403.301

x(2)=1.097



Program No: 6

Aim: Program to find the largest Eigen value using Power method.

#include

#include

#include

#define MAX 20

void main()

{

float a[MAX][MAX],x[MAX],s[MAX],epsilon;

float error,big_error,temp,lamda;int i,j,k,n;

clrscr();

printf("Enter number of eqautions:");

scanf("%d",&n);


for (i=1;i



s[i]=0.0;

for(j=1;jepsilon);

printf("\n\nLargest eigen value=%.4f\n",lamda);

printf("\nAssociated eigen vector is\n");

for(i=1;i



9

6

8

Enter required precision:2

Largest eigen value=12.0000

Associated eigen vector is

x(1)=1.0000

x(2)=1.1667



Program No: 7

Aim: Program to fit a polynomial of degree m through a set of points using

method of least squares.

#include

#include

#include

void main()

{

float x[20],y[20],a[20],c[20][20];

int i,j,n,m,k,m1,m2,l;

float p,q,max,temp,sum;

clrscr();

printf("Enter degree of polynomial:");

scanf("%d",&m);

printf("Enter number of points:");

scanf("%d",&n);

printf("Enter %d pair of values as x,y\n",n);for(i=1;i



{

c[i][j]=c[i][j]+pow((double)x[k],(double)l);

}

}

l=i-1;

c[i][m2]=0.0;

for(k=1;k



for(j=k;j=1;i--)

{

sum=0.0;

for(j=(i+1);j



Output:

Enter degree of polynomial:3

Enter number of points:2

Enter 2 pair of values as x,y

Enter value for x[2154]:23

Enter value for y[2154]:43

Enter value for x[2154]:23

Enter value for y[2154]:65

Regression coefficients

a[1]= 0.0000a[2]= 0.0000

a[3]= 0.1021

a[4]= 0.0000



Program No: 8

Aim: Program to implement Trapezoidal rule for tabulated function.

#include

#include

#include

#include

void main(){

int i,n;

float x[20],y[20],h,sum,integral;

clrscr();

printf("Enter number of intervals:");scanf("2%d",&n);

printf("Enter size of interval:");

scanf("%f",&h);

printf("Enter %d pair of (x,y)\n",n+1);

for(i=1;i



Program No: 9

Aim: Program to implement Simpsons 1/3 rule for tabulated function

#include

#include

#include

#include

void main(){

int i,n;

float x[20],y[20],h,sum,integral,s2,s4;

clrscr();

printf("Enter number of intervals:");scanf("%d",&n);


scanf("%f",&h);

printf("Enter %d pair of (x,y)\n",n+1);

for (i=1;i



Output:

Enter number of intervals:3

Enter size of interval:2

Enter 4 pair of (x,y)

4,3

3,4

2,7

9,5

Value of the integral= 16.0000



Program No: 10

Aim: Program to solve ODEof type dy/dx=xy using Eulers method.

#include

#include

float f(float x,float y)

{

return(x*y);

}

void main()

{int i;

float x,y,x1,y1,xf,h,s,s1,s2,s3,s4;

clrscr();

printf("Enter value of x1,y1,xf:");

scanf("%f,%f,%f",&x1,&y1,&xf);


scanf("%f",&h);

x=x1;

y=y1;

i=1;

printf("\n\nPoints constituting solution curve are\n\n");

printf("\nPoint x y");

printf("\n=================================");

printf("\n%3d\t%8.3f\t%8.3f",i,x,y);

while(x



}

Output:

Enter value of x1,y1,xf:2,3,4


Points constituting solution curve are

Point x y

=================================

1 2.000 3.000

2 4.000 15.000

===============================



Program No: 11

Aim: Program to solve ODE of type dy/dx=xy using second order Runge-Kutta

method(Heuns method).

#include

#include

float f(float x,float y)

{

return(x*y);

}

void main(){

int i;

float x,y,x1,y1,xf,h,s,s1,s2,s3,s4;

clrscr();

printf("Enter value of x1,y1,xf:");

scanf("%f,%f,%f",&x1,&y1,&xf);


scanf("%f",&h);

x=x1;

y=y1;

i=1;

printf("\n\nPoints constituting solution curve are\n\n");

printf("\nPoint x y");

printf("\n=================================");

printf("\n%3d\t%8.3f\t%8.3f",i,x,y);while(x


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}

printf("\n===============================\n");

getch();

}

Output:

Enter value of x1,y1,xf:4,5,3


Points constituting solution curve are

Point x y

=================================

1 4.000 5.000

===============================

Numerical Methods Practical Flle_MDU

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