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Category Archives: NUMERICAL

ANALYSIS and LINEARPROGRAMMING Lab Programs

Write a program to solve first order ordinary differential

equations (initial value problem) using adaptive Runge-

Kutta method .

Jun 26

Posted byjaisha57

#include

#include

#include

#include

float fun(float x,float y)

{

return(x*y);

}

void main(){

float y,x,h,e,k1,k2,k3,k4,k5,k;

int n,i;

clrscr();

printf(\n enter the value of x0:);

scanf(%f,&x);

printf(\n enter the value of y0:);

scanf(%f,&y);

printf(\n enter step length h: );

scanf(%f,&h);

printf(\n enter the vlaue of x at which y is needed :); scanf(%f,&e);

n=(e-x)/h;

for(i=1;i

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x=x+h;

printf(the value of y at x=%f is %f ,x,y);

}

getch();

}

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Write a program to solve first and second order ordinary

differential equations (initial value problem) using Runge-

Kutta fourth order method.

Jun 26

Posted byjaisha57

#include

#include

#include

#include

float fun(float x,float y)

{

return(x+fabs(sqrt(y)));

}void main()

{

float y,x,h,e,k1,k2,k3,k4,k;

int n,i;

clrscr();

printf(\n enter the value of x0:);

scanf(%f,&x);

printf(\n enter the value of y0:);

scanf(%f,&y);

printf(\n enter step length h: );

scanf(%f,&h);printf(\n enter the vlaue of x at which y is needed :);

scanf(%f,&e);

n=(e-x)/h;

for(i=1;i

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y=y+k;

x=x+h;

printf(\n the value of y at x=%f is %f,x,y);

}

getch();

}

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Write a program to solve the system of equations Ax = b

using Gauss-Seidel method

Jun 26

Posted byjaisha57

#include

#include

#include

#include

void main()

{

float a[20][20],x[20],e,big,temp,relerror,sum;

int n,i,j,maxit,itr;

char ch;

clrscr();

printf(enter the size of the equation:);

scanf(%d,&n);

top:for(i=1;i

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sum=sum+a[i][j]*x[j];

}

temp=(a[i][n+1]-sum)/a[i][i];

relerror=fabs((x[i]-temp)/temp);

if(relerror>big)

big=relerror;x[i]=temp;

}

if(big

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clrscr();

printf(enter the size of the equation);

scanf(%d,&n);

for(i=1;i

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{

sum=sum+a[i][j]*x[j];

}

x[i]=(a[i][n+1]-sum)/a[i][i];

printf(\nthe value of x%2d is %f\n,i,x[i]);

}getch();

}

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Write a program to solve the system of equations Ax = b in

tridiagonal form using Thomas Algorithm.

Jun 26

Posted byjaisha57

#include

#include

#include

#define MAX_N 20

void tridge(float a[],float b[],float c[],float f[],int i,int iflag);

void main()

{

float a[MAX_N+1],b[MAX_N+1],c[MAX_N+1],f[MAX_N+1];

int n,i,j,iflag;

clrscr();

printf(\n what is the order n of system ?);

scanf(%d,&n);

printf(\n give b[1],c[1],rhs[1] for equation 1:);

scanf(%f%f%f,&b[1],&c[1],&f[1]);

for(i=2;i

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return;

}

void tridge(float a[],float b[],float c[],float f[],int n,int iflag)

{

const float zero=0.0;

int j;if(iflag==0)

{

for(j=2;j

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{

return(1/(1+pow(x,2)));

}

void main()

{

float x0,x1,sum,result;int n,cho=0;

clrscr();

printf(enter the lower and upper limit \n);

scanf(%f%f,&x0,&x1);

printf(enter number of intervals:\n);

scan:scanf(%d,&n);

if(cho==0)

{

top:printf(\t enter choice \n);

printf(\n 1.for simpsons 1/3 rule\n);

printf(\n 2.for simpsons 3/8 rule\n);scanf(%d,&cho);

}

switch(cho)

{

case 1:if(n%2==0)

result=sim_1(x0,x1,n);

else

{

printf(wrong choice of interval);

printf(please enter even number);

goto scan;

}

break;

case 2:if(n%3==0)

result=sim_2(x0,x1,n);

else

{

printf(wrong choice of intervals \n );

printf(\n please enter a multiple of 3 \n);

goto scan;

}break;

default:printf(\n wrong choice enter again:);

goto top;

}

printf(\n the result=%f,result);

getch();

}

float sim_1(float x0,float x1,int n)

{

float result,h;

h=(x1-x0)/n;sum=fun(x0)+fun(x1);

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for(i=1;i

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printf(\n enter the lower and upper limits :);

scanf(%f%f,&x0,&x1);

printf(\n enter the number of intervals :);

scanf(%d,&n);

res=trap(x0,x1,n);

printf(\n TRAPEZOIDAL RULE =%f \n,res);getch();

}

float trap(float x0,float x1,int n)

{

float h,result;

h=(x1-x0)/n;

sum=fun(x0)+fun(x1);

for(i=1;i

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printf(\nx2=%f,x2);

for(i=1;x1!=x2;i++)

{

printf(\n(%d)%f,i,x2);

x1=x2;

x2=x1-(func(x1)/func1(x1));}

printf(\n the root is %f converge is %d approximately,x2,i);

getch();

return(0);

}

float func(float x)

{

return(pow(x,3)+(-2*x-5));

}

float func1(float x)

{return((3*pow(x,2)-2));

}

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Write a program to find the roots of an equation f (x) = 0

using Bisection method.

Jun 26

Posted byjaisha57

#include

#include

#include

float fun(float x)

{

return(pow(x,3)-x-1);}

void main()

{

float a,b,eps,x;

int i=0;

clrscr();

printf(\n enter the lower and upper limit );

scanf(%f%f,&a,&b);

printf(\n enter the epsilon value);

scanf(%f,&eps);

if((fun(a)*fun(b))>0)printf(\n starting value is unsuitable );

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else

while(fabs((b-a)/b)>eps)

{

x=(a+b)/2;

i++;

if((fun(x)*fun(a))>0)a=x;

else

b=x;

}

printf(\n solution converges to a root \n);

printf(\n number of iterationo=%d\n,i);

printf(%f\n,x);

getch();

}

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