Gauss-Jacobi Method using C

/*

 Gauss-Jacobi Method
 Equation:8x+2y-2z=0,x-8y+3y=-4,2x+y+9z=12
*/
#include<conio.h>
#include<stdio.h>
void main()
{
 float ax,ay,az,x,y,z;
 int i,n;
 float f1(float,float);
 float f2(float,float);
 float f3(float,float);
 clrscr();
 printf("\nEnter the number of equations:: ");
 scanf("%d",&n);
 x=y=z=0;
 for(i=0;i<=n;i++)
 {
  ax=f1(y,z);
  ay=f2(z,x);
  az=f3(x,y);
  x=ax;
  y=ay;
  z=az;
 }
 printf("\nx= %f, y= %f, z= %f",x,y,z);
 getch();
}
float f1(float y,float z)
{
 return (8-2*y+2*z)/8;
}
float f2(float z,float x)
{
 return (4+x+3*z)/8;
}
float f3(float x,float y)
{
 return (12-2*x-y)/9;
}

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Gauss-Seidal Method using C

/*

 Gauss-Seidal Method
 Equation:8x+2y-2z=0,x-8y+3y=-4,2x+y+9z=12
*/
#include<conio.h>
#include<stdio.h>
void main()
{
 float ax,ay,az,x,y,z;
 int i,n;
 float f1(float,float);
 float f2(float,float);
 float f3(float,float);
 clrscr();
 printf("\nEnter the number of equations:: ");
 scanf("%d",&n);
 x=y=z=0;
 for(i=0;i<=n;i++)
 {
  ax=f1(y,z);
  ay=f2(z,ax);
  az=f3(ax,ay);
  x=ax;
  y=ay;
  z=az;
 }
 printf("\nx= %f, y= %f, z= %f",x,y,z);
 getch();
}
float f1(float y,float z)
{
 return (8-2*y+2*z)/8;
}
float f2(float z,float x)
{
 return (4+x+3*z)/8;
}
float f3(float x,float y)
{
 return (12-2*x-y)/9;
}

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Newtons forward formula Using C

/*

Newtons forward formula
x: 1 1.10 1.20 1.30
y: .4158 .8912 .9320 .9636
Compute::f(1.02)=?
*/
#include<conio.h>
#include<stdio.h>
#define n 4
void main()
{
 float x[n],y[n][n],xf,fx,u,h;
 int j,i,index,f=1;
 for(i=0;i<n;i++)
 {
 printf("\nEnter x[%d] & y[%d][0]",i+1,i+1);
 scanf("%f%f",&x[i],&y[i][0]);
 }
 for(j=1;j<n;j++)
 {
 for(i=0;i<n;i++)
 y[i][j]=y[i+1][j-1]-y[i][j-1];
 }
 for(i=0;i<n;i++)
 {
 for(j=0;j<n-1;j++)
  printf("%f\t",y[i][j]);
 printf("\n");
 }
 printf("\nEnter x");
 scanf("%f",&xf);
 for(i=0;i<n-1;i++)
 {
 if(xf>=x[i]&&xf<=x[i+1])
 {
  index=i;
  break;
 }
 }
 h=x[1]-x[0];
 u=(xf-x[index])/h;
 fx=y[index][0];
 for(i=1;i<n;i++)
 {
 if(i!=1)
    u=u*(u+1-i);
 f=f*i;
 fx=fx+(u*y[index][i])/f;
 }

 printf("\nResult %f",fx);
 getch();
}

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Newtons backward formula using C

/*

Newtons backward formula
x: 1 1.10 1.20 1.30
y: .4158 .8912 .9320 .9636
Compute::f(1.40)=?
*/
#include<conio.h>
#include<stdio.h>
#define n 4
void main()
{
 float x[n],y[n][n],xf,fx,u,h;
 int j,i,index,f=1;
 for(i=0;i<n;i++)
 {
 printf("\nEnter x[%d] & y[%d][0]",i+1,i+1);
 scanf("%f%f",&x[i],&y[i][0]);
 }
 for(j=1;j<n;j++)
 {
 for(i=0;i<n;i++)
 y[i][j]=y[i+1][j-1]-y[i][j-1];
 }
 for(i=0;i<n;i++)
 {
 for(j=0;j<n-1;j++)
  printf("%f\t",y[i][j]);
 printf("\n");
 }
 printf("\nEnter x");
 scanf("%f",&xf);
 index=n-1; 
 h=x[1]-x[0];
 u=(xf-x[index])/h;
 fx=y[index][0];
 for(i=1;i<n;i++)
 {
 if(i!=1)
    u=u*(u+i-1);
 f=f*i;
 fx=fx+(u*y[index][i])/f;
 }

 printf("\nResult %f",fx);
 getch();
}

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Lagranges formula using C

/*

Lagranges formula
x: 30 35 45 55
y: 148 196 68 34
Compute::f(40)=?
*/
#include<conio.h>
#include<stdio.h>
#define n 4
void main()
{
 float f,x[n],y[n],xf,fx;
 int j,i;
 for(i=0;i<n;i++)
 {
 printf("\nEnter x[%d] & y[%d]",i+1,i+1);
 scanf("%f%f",&x[i],&y[i]);
 }
 printf("\nEnter x");
 scanf("%f",&xf);
 fx=0;
 for(i=0;i<n;i++)
 {
  f=1;
  for(j=0;j<n;j++)
  {
 if(i!=j)
 f=f*((xf-x[j])/(x[i]-x[j]));
  }
  fx=fx+(f*y[i]);
 }
 printf("\nResult %f",fx);
 getch();
}

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Runga-Kutta Method using C

/*

Runga-Kutta Method
COmpute:: f(0.2)=?
When f(x,y)=x+y^2; y(0)=1 h=0.1
*/
#include<conio.h>
#include<stdio.h>

void main()
{
 float x,y,h,xf,k1,k2,k3,k4,n;
 int i;
 float f(float,float);
 printf("\nEnter x0 & y0");
 scanf("%f%f",&x,&y);
 printf("\nEnter x & h");
 scanf("%f%f",&xf,&h);
 n=(xf-x)/h;
 for(i=0;i<=(int)n;i++)
 {
 k1=h*f(x,y);
 k2=h*f(x+h/2,y+k1/2);
 k3=h*f(x+h/2,y+k2/2);
 k4=h*f(x+h,y+k3);
 y=y+(k1+2*(k2+k3)+k4)/6;
 x=x+h;
 }
 printf("\nResult %f",y);
 getch();
}
float f(float x,float y)
{
 return x+y*y;
}

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C Program to solve using Euler Rule

/*
Euler Rule 
Compute:: f(0.1)=?
When f(x,y)=1+xy, y(0)=2,h=0.01
*/
#include<conio.h>
#include<stdio.h>

void main()
{
 float x0,y0,h,xf,fx,x;
 float f(float,float);
 printf("\nEnter x0 & y0");
 scanf("%f%f",&x0,&y0);
 printf("\nEnter x & h");
 scanf("%f%f",&x,&h);
 xf=x0;fx=y0;
 while(xf<=x)
 {
 fx=fx+h*f(xf,fx);
 xf=xf+h;
 }
 printf("\nResult %f",fx);
 getch();
}

float f(float x,float y)
{
 return 1+x*y;
}

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C Program to implement Simpson's 1/3 rd Rule

/*

 Simpson's 1/3 Rule
 Equation: x/(1+x) dx
 lower limit=0 upper limit=1 number of interval=6
*/
#include<conio.h>
#include<stdio.h>
void main()
{
 float a,b,h,x,y,so=0;
 float x0,y0,yn,xn,r,se=0;;
 int i,n;
 float f(float);
 clrscr();
 printf("\nEnter lower limit value:: ");
 scanf("%f",&a);
 printf("\nEnter upper limit value:: ");
 scanf("%f",&b);
 printf("\nEnter the number of intervals:: ");
 scanf("%d",&n);
 h=(b-a)/n;
 x0=a;
 y0=f(x0);
 yn=f(b);
 x=x0+h;
 for(i=1;i<=n-1;i=i+2)
 {
  y=f(x);
  so=so+y;
  x=x+2*h;
 }
 x=x0+2*h;
 for(i=2;i<=n-2;i=i+2)
 {
  y=f(x);
  se=se+y;
  x=x+2*h;
 }
 r=(h/3)*(y0+yn+4*so+2*se);
 printf("\nResult is:: %f",r);
 getch();
}
float f(float x)
{
 return x/(1+x);
}

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C Program to implement Trapezoidal Rule

/*
 Trapezoidal Rule
 Equation: x/(1+x) dx
 lower limit=0  upper limit=1 number of interval=6
*/
#include<conio.h>
#include<stdio.h>
void main()
{
 float a,b,h,x,y,s=0;
 float x0,y0,xn,yn,r;
 int i,n;
 float f(float);
 clrscr();
 printf("\nEnter lower limit value:: ");
 scanf("%f",&a);
 printf("\nEnter upper limit value:: ");
 scanf("%f",&b);
 printf("\nEnter the number of intervals:: ");
 scanf("%d",&n);
 h=(b-a)/n;
 x0=a;
 y0=f(a);
 yn=f(b);
 x=x0+h;
 for(i=1;i<=n-1;i++)
 {
  y=f(x);
  s=s+y;
  x=x+h;
 }
 r=(h/2)*(y0+yn+2*s);
 printf("\nResult is:: %f",r);
 getch();
}
float f(float x)
{
 return x/(1+x);
}

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Implement Secant Method using C

/*

 Secant Method

 Equation: x^3-4x-9=0
*/
#include<conio.h>
#include<stdio.h>
void main()
{
 float a,b,k,c;
 int i;
 float f(float);
 clrscr();
 printf("\nEnter first initial value:: ");
 scanf("%f",&a);
 printf("\nEnter second initial value:: ");
 scanf("%f",&b);
 for(i=1;i<=5;i++)
 {
  c=b-((b-a)*(f(b)/(f(b)-f(a))));
  a=b;
  b=c;
 }
 printf("\nRoot is:: %f",c);
 getch();
}
float f(float x)
{
 return (x*x*x)-(4*x)-9;
}

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Method of Regula-Falsi using C

/*

 Method of Regula-Falsi

 Equation: x^3-4x-9=0
*/
#include<conio.h>
#include<stdio.h>

void main()
{
 float a,b,k,c;
 int i;
 float f(float);
 clrscr();
 printf("\nEnter first initial value:: ");
 scanf("%f",&a);
 printf("\nEnter second initial value:: ");
 scanf("%f",&b);
 for(i=1;i<=5;i++)
 {
  c=b-((b-a)*(f(b)/(f(b)-f(a))));
  k=f(c);
  if(k>0)
 b=c;
  if(k<=0)
 a=c;
 }
 printf("\nRoot is:: %f",c);
 getch();
}
float f(float x)
{
 return (x*x*x)-(4*x)-9;
}

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Implement Newton-Raphson Method using C

/*

 Method of Newton-Raphson

 Equation: x^3-4x-9=0
*/

#include<stdio.h>

void main()
{
 float a,h;
 int i;
 float f(float);
 float f1(float);
 printf("\nEnter initial value:: ");
 scanf("%f",&a);
 for(i=1;i<=5;i++)
 {
  h=-f(a)/f1(a);
  a=a+h;
 }
 printf("\nRoot is:: %f",a);
}
float f(float x)
{
 return (x*x*x)-(4*x)-9;
}
float f1(float x)
{
 return (3*x*x)-4;
}

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