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 <string.h>
# include <stdlib.h>
# include <conio.h>
# include <math.h>
const int max_size=30;
int top=-1;
int iterations=0;
long double x0=0;
long double xn=0;
char Non_linear_equation[100]={NULL};
char Stack[max_size][max_size]={NULL};
char Postfix_expression[max_size][max_size]={NULL};
//----------------------- Function Prototypes -------------------------//
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_non_linear_equation( );
void apply_simple_itrative_method( );
void show_result( );
//------------------------------ main( ) ------------------------------//
int main( )
{
clrscr( );
textmode(C4350);
show_screen( );
get_input_non_linear_equation( );
apply_simple_itrative_method( );
show_result( );
getch( );
return 0;
}
//---------------------- Function Definitions -------------------------//
//-------------------------- 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;
}
//-------------------------- show_screen( ) ---------------------------//
void show_screen( )
{
cprintf(\"\\n********************************************************************************\");
cprintf(\"*************************- -***************************\");
cprintf(\"*------------------------- \");
textbackground(1);
cprintf(\" Simple Itrative Method \");
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);
}
//------------------- get_input_non_linear_equation( ) -----------------//
void get_input_non_linear_equation( )
{
gotoxy(4,11);
cout<<\"Non-Linear Equation with One Variable:\";
gotoxy(4,12);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
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(4,14);
cout<<\"Enter the Function with variabel x = f(x) = \";
cin>>Non_linear_equation;
gotoxy(4,17);
cout<<\"Enter the Starting value = x0 = \";
cin>>x0;
gotoxy(4,20);
cout<<\"Enter the number of iterations = \";
cin>>iterations;
gotoxy(1,2);
}
//------------------ apply_simple_itrative_method( ) ------------------//
void apply_simple_itrative_method( )
{
clear_screen( );
gotoxy(4,10);
cout<<\"Solution :\";
gotoxy(4,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍ\";
convert_infix_expression_to_postfix_expression(Non_linear_equation);
gotoxy(4,13);
cout<<\"ÚÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿\";
gotoxy(4,14);
cout<<\"³ n ³ Xn ³\";
gotoxy(4,15);
cout<<\"ÃÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";
gotoxy(4,16);
cout<<\"³ ³ ³\";
xn=x0;
long double fx=0;
int x_cord=4;
int y_cord=17;
for(int count_1=1;count_1<=iterations;count_1++)
{
gotoxy(x_cord,y_cord);
cout<<\"³ ³ ³\";
gotoxy(x_cord,(y_cord+1));
cout<<\"³ ³ ³\";
gotoxy((x_cord+4),y_cord);
cout<<count_1;
fx=evaluate_postfix_expression(xn);
xn=fx;
gotoxy((x_cord+13),y_cord);
cout<<fx;
y_cord+=2;
if((count_1%12)==0 && count_1<iterations)
{
y_cord=17;
gotoxy(30,44);
cout<<\"Press any key to continue...\";
getch( );
for(int count_2=1;count_2<25;count_2++)
{
gotoxy(3,(16+count_2));
cout<<\" \";
}
}
}
gotoxy(x_cord,y_cord);
cout<<\"ÀÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ\";
gotoxy(30,44);
cout<<\"Press any key to continue...\";
getch( );
}
//--------------------------- show_result( ) --------------------------//
void show_result( )
{
clear_screen( );
gotoxy(6,10);
cout<<\"Function of Non-Linear Equation :\";
gotoxy(6,11);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(10,13);
cout<<\"f(x) = \"<<Non_linear_equation;
gotoxy(6,17);
cout<<\"Starting Value = x0 = \"<<x0;
gotoxy(6,19);
cout<<\"Number of Iterations = \"<<iterations;
gotoxy(6,25);
cout<<\"Required Root :\";
gotoxy(6,26);
cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";
gotoxy(10,28);
cout<<\"x = \"<<xn;
gotoxy(1,2);
}
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Program to read a Non-Linear equation in one variable, then evaluate it using Simple Itrative Method and display its kD accurate root
