Numerical Analysis Programs
Non-Linear Equations
Difference Table 3rd Deriv - Ctral Diff fmla - odr 4 Euler Method Gauss Elimination Method Cubic Spline Secant Method 2nd Deriv - Ctral Diff fmla - odr 4 Romberg MethodNumerical Integration
Newton\'s Backward Diff Intrpl fmla Modified False-Position Method 1st Deriv - Ctral Diff fmla - odr 4 Trapezoidal RuleSpline Functions
Newton\'s Divided Diff Intrpl fmla Runge-Kutta Methods Bisection Method 1st Deriv. - Backward Diff fmla. 4th Deriv - Ctral Diff fmla - odr 2Finite Differences
Divided Difference Table Mid-Point Method Jacobi Iterative Method Natural Cubic Spline InterpolantLinear System of Equations
Simple Itrative Method 3rd Deriv - Ctral Diff fmla - odr 2 Gussian Quadrature RuleOrdinary Differential Equations
Newton-Raphson Method Newton-Raphson Method 2nd Deriv - Ctral Diff fmla - odr 2 Simpson\'s 1/3 RuleNumerical Differentiation
Newton\'s Forward Diff Intrpl fmla False-Position Method 1st Deriv. - Central Diff fmla. 4th Deriv - Ctral Diff fmla - odr 4Interpolation
Lagrange\'s Interpolation Formula Euler-Trapezoidal Rule Guass-Seidel Iterative Method Clamped Cubic Spline Interpolant
# include <iostream.h>
# include <stdlib.h>
# include <string.h>
# include <stdio.h>
# include <conio.h>
# include <math.h>
const int max_size=13;
int n=0;
int top=-1;
int choice=0;
long double xn[max_size]={0};
long double px[max_size]={0};
long double dd_table[max_size][max_size]={0};
char Non_linear_equation[100]={NULL};
char Stack[30][30]={NULL};
char Postfix_expression[30][30]={NULL};
void push(const char *);
void convert_infix_expression_to_postfix_expression(const char *);
const char* pop( );
const long double evaluate_postfix_expression(const long double);
void show_screen( );
void clear_screen( );
void get_input( );
void construct_dd_table( );
void show_dd_table( );
void compute_newtons_dd_interpolation_polynomial( );
void estimate_pnx( );
int main( )
{
clrscr( );
textmode(C4350);
show_screen( );
get_input( );
construct_dd_table( );
show_dd_table( );
compute_newtons_dd_interpolation_polynomial( );
estimate_pnx( );
return 0;
}
//-------------------------- show_screen( ) ---------------------------//
void show_screen( )
{
cprintf(\"\\n********************************************************************************\");
cprintf(\"*************- -************\");
cprintf(\"*------------- \");
textbackground(1);
cprintf(\" Newton\'s Divided Difference Interpolation Formula \");
textbackground(8);
cprintf(\" ------------*\");
cprintf(\"*************- -************\");
cprintf(\"********************************************************************************\");
for(int count=0;count<42;count++)
cprintf(\"* *\");
gotoxy(1,46);
cprintf(\"********************************************************************************\");
cprintf(\"*------------------------------------------------------------------------------*\");
cprintf(\"********************************************************************************\");
gotoxy(1,2);
}
//------------------------- clear_screen( ) ---------------------------//
void clear_screen( )
{
for(int count=0;count<37;count++)
{
gotoxy(3,8+count);
cout<<\" \";
}
gotoxy(1,2);
}
//-------------------------- push(const char*) ------------------------//
void push(const char* Operand)
{
if(top==(max_size-1))
{
cout<<\"Error : Stack is full.\"<<endl;
cout<<\"\\n Press any key to exit.\";
getch( );
exit(0);
}
else
{
top++;
strcpy(Stack[top],Operand);
}
}
//------------------------------ pop( ) -------------------------------//
const char* pop( )
{
char Operand[40]={NULL};
if(top==-1)
{
cout<<\"Error : Stack is empty.\"<<endl;
cout<<\"\\n Press any key to exit.\";
getch( );
exit(0);
}
else
{
strcpy(Operand,Stack[top]);
strset(Stack[top],NULL);
top--;
}
return Operand;
}
//---- convert_infix_expression_to_postfix_expression(const char*) ----//
void convert_infix_expression_to_postfix_expression(const char* Expression)
{
char Infix_expression[100]={NULL};
char Symbol_scanned[30]={NULL};
push(\"(\");
strcpy(Infix_expression,Expression);
strcat(Infix_expression,\"+0)\");
int flag=0;
int count_1=0;
int count_2=0;
int equation_length=strlen(Infix_expression);
if(Infix_expression[0]==\'(\')
flag=1;
do
{
strset(Symbol_scanned,NULL);
if(flag==0)
{
int count_3=0;
do
{
Symbol_scanned[count_3]=Infix_expression[count_1];
count_1++;
count_3++;
}
while(count_1<=equation_length &&
Infix_expression[count_1]!=\'(\' &&
Infix_expression[count_1]!=\'+\' &&
Infix_expression[count_1]!=\'-\' &&
Infix_expression[count_1]!=\'*\' &&
Infix_expression[count_1]!=\'/\' &&
Infix_expression[count_1]!=\'^\' &&
Infix_expression[count_1]!=\')\');
flag=1;
}
else if(flag==1)
{
Symbol_scanned[0]=Infix_expression[count_1];
count_1++;
if(Infix_expression[count_1]!=\'(\' &&
Infix_expression[count_1]!=\'^\' &&
Infix_expression[count_1]!=\'*\' &&
Infix_expression[count_1]!=\'/\' &&
Infix_expression[count_1]!=\'+\' &&
Infix_expression[count_1]!=\'-\' &&
Infix_expression[count_1]!=\')\')
flag=0;
if(Infix_expression[count_1-1]==\'(\' &&
(Infix_expression[count_1]==\'-\' ||
Infix_expression[count_1]==\'+\'))
flag=0;
}
if(strcmp(Symbol_scanned,\"(\")==0)
push(\"(\");
else if(strcmp(Symbol_scanned,\")\")==0)
{
while(strcmp(Stack[top],\"(\")!=0)
{
strcpy(Postfix_expression[count_2],pop( ));
count_2++;
}
pop( );
}
else if(strcmp(Symbol_scanned,\"^\")==0 ||
strcmp(Symbol_scanned,\"+\")==0 ||
strcmp(Symbol_scanned,\"-\")==0 ||
strcmp(Symbol_scanned,\"*\")==0 ||
strcmp(Symbol_scanned,\"/\")==0)
{
if(strcmp(Symbol_scanned,\"^\")==0)
{ }
else if(strcmp(Symbol_scanned,\"*\")==0 ||
strcmp(Symbol_scanned,\"/\")==0)
{
while(strcmp(Stack[top],\"^\")==0 ||
strcmp(Stack[top],\"*\")==0 ||
strcmp(Stack[top],\"/\")==0)
{
strcpy(Postfix_expression[count_2],pop( ));
count_2++;
}
}
else if(strcmp(Symbol_scanned,\"+\")==0 ||
strcmp(Symbol_scanned,\"-\")==0)
{
while(strcmp(Stack[top],\"(\")!=0)
{
strcpy(Postfix_expression[count_2],pop( ));
count_2++;
}
}
push(Symbol_scanned);
}
else
{
strcat(Postfix_expression[count_2],Symbol_scanned);
count_2++;
}
}
while(strcmp(Stack[top],NULL)!=0);
strcat(Postfix_expression[count_2],\"=\");
count_2++;
}
//---------- evaluate_postfix_expression(const long double) -----------//
const long double evaluate_postfix_expression(const long double x)
{
long double function_value=0;
int count_1=-1;
char Symbol_scanned[30]={NULL};
do
{
count_1++;
strcpy(Symbol_scanned,Postfix_expression[count_1]);
if(strcmp(Symbol_scanned,\"^\")==0 ||
strcmp(Symbol_scanned,\"*\")==0 ||
strcmp(Symbol_scanned,\"/\")==0 ||
strcmp(Symbol_scanned,\"+\")==0 ||
strcmp(Symbol_scanned,\"-\")==0)
{
char Result[30]={NULL};
char Operand[2][30]={NULL};
strcpy(Operand[0],pop( ));
strcpy(Operand[1],pop( ));
long double operand[2]={0};
long double result=0;
char *endptr;
for(int count_2=0;count_2<2;count_2++)
{
int flag=0;
if(Operand[count_2][0]==\'-\')
{
int length=strlen(Operand[count_2]);
for(int count_3=0;count_3<(length-1);count_3++)
Operand[count_2][count_3]=Operand[count_2][(count_3+1)];
Operand[count_2][count_3]=NULL;
flag=1;
}
if(strcmp(Operand[count_2],\"x\")==0)
operand[count_2]=x;
else if(strcmp(Operand[count_2],\"e\")==0)
operand[count_2]=2.718282;
else if(strcmp(Operand[count_2],\"sinx\")==0)
operand[count_2]=sinl(x);
else if(strcmp(Operand[count_2],\"cosx\")==0)
operand[count_2]=cosl(x);
else if(strcmp(Operand[count_2],\"tanx\")==0)
operand[count_2]=tanl(x);
else if(strcmp(Operand[count_2],\"lnx\")==0)
operand[count_2]=logl(x);
else if(strcmp(Operand[count_2],\"logx\")==0)
operand[count_2]=log10l(x);
else
operand[count_2]=strtod(Operand[count_2],&endptr);
if(flag)
operand[count_2]*=-1;
}
switch(Symbol_scanned[0])
{
case \'^\' : result=powl(operand[1],operand[0]);
break;
case \'*\' : result=operand[1]*operand[0];
break;
case \'/\' : result=operand[1]/operand[0];
break;
case \'+\' : result=operand[1]+operand[0];
break;
case \'-\' : result=operand[1]-operand[0];
break;
}
gcvt(result,25,Result);
push(Result);
}
else if(strcmp(Symbol_scanned,\"=\")!=0)
push(Symbol_scanned);
}
while(strcmp(Symbol_scanned,\"=\")!=0);
char Function_value[30]={NULL};
char *endptr;
strcpy(Function_value,pop( ));
function_value=strtod(Function_value,&endptr);
return function_value;
}
//----------------------------- get_input( ) --------------------------//
void get_input( )
{
do
{
clear_screen( );
gotoxy(6,9);
cout<<\"Number of Distinct Data Points :\";
gotoxy(6,10);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(27,13);
cout<<\"[ min. n = 2 | max. n = 12 ]\";
gotoxy(6,12);
cout<<\"Enter the max. number of distinct data points = n = \";
cin>>n;
if(n<2 || n>12)
{
gotoxy(12,25);
cout<<\"Error : Wrong Input. Press <Esc> to exit or any other key\";
gotoxy(12,26);
cout<<\" to try again.\";
n=int(getche( ));
if(n==27)
exit(0);
}
}
while(n<2 || n>12);
gotoxy(6,19);
cout<<\"Input Mode :\";
gotoxy(6,20);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(8,23);
cout<<\"Press : \";
gotoxy(10,25);
cout<<\"- \'Y\' or <Enter> to enter function\";
gotoxy(10,27);
cout<<\"- \'N\' or <Any other key> to enter values of the function\";
gotoxy(8,30);
cout<<\"Enter your choice : \";
char Choice=NULL;
Choice=getch( );
if(Choice==\'y\' || Choice==\'Y\' || int(Choice)==13)
{
choice=1;
gotoxy(28,30);
cout<<\"Y\";
}
else
{
gotoxy(28,30);
cout<<\"N\";
}
gotoxy(25,43);
cout<<\"Press any key to continue...\";
getch( );
if(choice)
{
clear_screen( );
gotoxy(6,11);
cout<<\"Non-Linear Function :\";
gotoxy(6,12);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(6,37);
cout<<\"Note : Write the function with proper Braces ( ) e.g; 2x+3 as (2*x)+3\";
gotoxy(6,40);
cout<<\"Available Operators : ^ (raised to power) , * , / , + , -\";
gotoxy(6,42);
cout<<\"Available Operands : x , e , sinx , cosx , tanx , lnx , logx ,\";
gotoxy(6,44);
cout<<\" n = any number\";
gotoxy(6,14);
cout<<\"Enter the Function : f(x) = \";
cin>>Non_linear_equation;
convert_infix_expression_to_postfix_expression(Non_linear_equation);
}
clear_screen( );
gotoxy(6,9);
cout<<\"Data Points & Values of Function :\";
gotoxy(6,10);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(25,12);
cout<<\"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿\";
gotoxy(25,13);
cout<<\"³ x ³ f(x) ³\";
gotoxy(25,14);
cout<<\"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy(25,15);
cout<<\"³ ³ ³\";
for(int count_1=0;count_1<n;count_1++)
{
gotoxy(25,(wherey( )+1));
cout<<\"³ ³ ³\";
gotoxy(25,(wherey( )+1));
cout<<\"³ ³ ³\";
}
gotoxy(25,(wherey( )+1));
cout<<\"ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ\";
gotoxy(25,16);
for(int count_2=0;count_2<n;count_2++)
{
gotoxy(27,wherey( ));
cin>>xn[count_2];
if(choice)
{
dd_table[0][count_2]=evaluate_postfix_expression(xn[count_2]);
gotoxy(43,(wherey( )-1));
cout<<dd_table[0][count_2];
}
else
{
gotoxy(43,(wherey( )-1));
cin>>dd_table[0][count_2];
}
if(choice)
gotoxy(25,(wherey( )+2));
else
gotoxy(25,(wherey( )+1));
}
gotoxy(25,43);
cout<<\"Press any key to continue...\";
getch( );
}
//----------------------- construct_dd_table( ) -----------------------//
void construct_dd_table( )
{
for(int count_1=1;count_1<n;count_1++)
{
for(int count_2=count_1;count_2<n;count_2++)
{
long double fx1=dd_table[(count_1-1)][(count_2-1)];
long double fx2=dd_table[(count_1-1)][count_2];
long double x1=xn[(count_2-count_1)];
long double x2=xn[count_2];
dd_table[count_1][count_2]=((fx2-fx1)/(x2-x1));
}
}
}
//-------------------------- show_dd_table( ) -------------------------//
void show_dd_table( )
{
clear_screen( );
gotoxy(4,10);
cout<<\"Divided Difference Table :\";
gotoxy(4,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(4,13);
cout<<\"ÚÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy(4,14);
cout<<\"³ x ³ f(x) \";
gotoxy(4,15);
cout<<\"ÃÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy(4,16);
cout<<\"³ ³ \";
int x_cord=4;
int y_cord=17;
for(int count_1=0;count_1<n;count_1++)
{
gotoxy(x_cord,y_cord);
cout<<\"³ ³ \";
gotoxy(x_cord,(y_cord+1));
cout<<\"³ ³ \";
gotoxy((x_cord+2),y_cord);
cout<<xn[count_1];
gotoxy((x_cord+11),y_cord);
cout<<dd_table[0][count_1];
y_cord+=2;
}
gotoxy(x_cord,y_cord);
cout<<\"ÀÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
x_cord=28;
int count_2=0;
for(int count_3=1;count_3<n;count_3++)
{
gotoxy(x_cord,13);
cout<<\"ÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy(x_cord,14);
cout<<\"³\";
gotoxy(x_cord,15);
cout<<\"ÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy(x_cord,16);
cout<<\"³\";
gotoxy(x_cord,y_cord);
cout<<\"ÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy((x_cord+6),14);
cout<<count_3;
if(count_3==1)
cout<<\"st\";
else if(count_3==2)
cout<<\"nd\";
else if(count_3==3)
cout<<\"rd\";
else
cout<<\"th\";
y_cord=17;
for(int count_4=0;count_4<n;count_4++)
{
gotoxy(x_cord,y_cord);
cout<<\"³\";
gotoxy(x_cord,(y_cord+1));
cout<<\"³\";
if(count_4>=count_3)
{
gotoxy((x_cord+2),(y_cord-count_3));
cout<<dd_table[count_3][count_4];
}
y_cord+=2;
}
x_cord+=16;
count_2++;
if((count_2%3)==0 && count_3<(n-1))
{
gotoxy(x_cord,13);
cout<<\"ÂÄÄ\";
gotoxy(x_cord,14);
cout<<\"³\";
gotoxy(x_cord,15);
cout<<\"ÅÄÄ\";
gotoxy(x_cord,16);
cout<<\"³\";
gotoxy(x_cord,y_cord);
cout<<\"ÁÄÄ\";
y_cord=17;
for(int count_5=0;count_5<n;count_5++)
{
gotoxy(x_cord,y_cord);
cout<<\"³\";
gotoxy(x_cord,(y_cord+1));
cout<<\"³\";
y_cord+=2;
}
gotoxy(30,44);
cout<<\"Press any key to continue...\";
getch( );
y_cord=13;
x_cord=28;
for(int count_6=0;count_6<=(n+2);count_6++)
{
gotoxy(x_cord,y_cord);
cout<<\" \";
gotoxy(x_cord,(y_cord+1));
cout<<\" \";
y_cord+=2;
}
y_cord-=2;
count_2=0;
count_3--;
}
}
gotoxy(x_cord,13);
cout<<\"¿\";
gotoxy(x_cord,14);
cout<<\"³\";
gotoxy(x_cord,16);
cout<<\"³\";
y_cord=17;
for(int count_6=0;count_6<n;count_6++)
{
gotoxy(x_cord,y_cord);
cout<<\"³\";
gotoxy(x_cord,(y_cord+1));
cout<<\"³\";
y_cord+=2;
}
gotoxy(x_cord,15);
cout<<\"\";
gotoxy(x_cord,y_cord);
cout<<\"Ù\";
gotoxy(30,44);
cout<<\"Press any key to continue...\";
getch( );
}
//--------- compute_newtons_dd_interpolation_polynomial( ) ------------//
void compute_newtons_dd_interpolation_polynomial( )
{
for(int count_1=0;count_1<n;count_1++)
xn[count_1]=(xn[count_1]*(-1));
px[0]=dd_table[0][0];
for(int count_2=1;count_2<n;count_2++)
{
long double fx[max_size]={0};
fx[0]=xn[0];
fx[1]=1;
for(int count_3=0;count_3<(count_2-1);count_3++)
{
fx[(count_3+2)]=1;
for(int count_4=(1+count_3);count_4>0;count_4--)
{
fx[count_4]*=xn[(count_3+1)];
fx[count_4]+=fx[(count_4-1)];
}
fx[0]*=xn[(count_3+1)];
}
for(int count_5=0;count_5<(count_2+1);count_5++)
fx[count_5]*=dd_table[count_2][count_2];
for(int count_6=0;count_6<(count_2+1);count_6++)
px[count_6]+=fx[count_6];
}
}
//---------------------------- estimate_pnx( ) ------------------------//
void estimate_pnx( )
{
clear_screen( );
gotoxy(6,10);
cout<<\"Newton\'s Divided Difference Interpolation Formula :\";
gotoxy(6,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(10,13);
cout<<\"P\"<<(n-1)<<\"(x) = \";
for(int count_1=(n-1);count_1>=0;count_1--)
{
if(count_1==(n-1) && n>2)
cout<<px[count_1]<<\" x\"<<count_1;
else if(count_1>1)
cout<<fabs(px[count_1])<<\" x\"<<count_1;
else if(count_1==1)
cout<<fabs(px[count_1])<<\" x\";
else if(count_1==0)
cout<<fabs(px[count_1]);
if(wherex( )>=70)
gotoxy(30,(wherey( )+2));
if(count_1>0)
{
if(px[(count_1-1)]>0)
cout<<\" + \";
else
cout<<\" - \";
}
if(wherex( )>=70)
gotoxy(30,(wherey( )+2));
}
gotoxy(6,19);
cout<<\"Estimation of Pn(x) :\";
gotoxy(6,20);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
char Choice=NULL;
long double x=0;
long double pnx=0;
do
{
Choice=NULL;
x=0;
pnx=0;
gotoxy(10,22);
cout<<\"Enter the value of x = \";
cin>>x;
pnx=px[0];
pnx+=(px[1]*x);
for(int count_2=2;count_2<n;count_2++)
{
long double temp=x;
for(int count_3=1;count_3<count_2;count_3++)
temp*=x;
pnx+=(px[count_2]*temp);
}
gotoxy(10,26);
cout<<\"The estimated value of P\"<<(n-1)<<\"(\"<<x<<\") = \"<<pnx;
if(choice)
{
long double fx=0;
fx=evaluate_postfix_expression(x);
gotoxy(10,28);
cout<<\"The Actual value of f\"<<\"(\"<<x<<\") = \"<<fx;
gotoxy(10,30);
cout<<\"Absolute Error = E(abs) = \"<<fabs((fx-pnx));
}
gotoxy(15,40);
cout<<\"Press <Esc> to exit, \'V\' to view D.D. Table again\";
gotoxy(25,42);
cout<<\"or any other key to continue...\";
Choice=getch( );
if(int(Choice)!=27 && Choice!=\'v\' && Choice!=\'V\')
{
gotoxy(10,22);
cout<<\" \";
gotoxy(10,26);
cout<<\" \";
gotoxy(10,28);
cout<<\" \";
gotoxy(10,30);
cout<<\" \";
gotoxy(15,40);
cout<<\" \";
gotoxy(25,42);
cout<<\" \";
}
else if(Choice==\'v\' || Choice==\'V\')
{
show_dd_table( );
estimate_pnx( );
}
else if(int(Choice)==27)
exit(0);
}
while(1);
}
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Menu driven Bank Application Project
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Menu driven telephone directory program
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Program to addition of two polynomial
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PROGRAM TO DISPLAY MESSAGE USING COUT
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Program that prints first 20 integers (using while loop)
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Program that prints all the even numbers b/w 0 to 50 ( using while, do-while and for loop )
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Comment line in c
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Program that reads an expression consisting of two non-negative integer and an operator. Determine if either integer or the result of the expres......
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Program to estimate the value of Third Derivative of the function at the given points from the given data using Central Difference Formula of order 2
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Program to construct Newtons Divided Difference Interpolation Formula from the given distinct data points and estimate the value of the function
