Write a C Program to implement Simpson method.
Simpson method is used for approximating integral of the function.
Simpson’s rule also corresponds to the 3-point Newton-Cotes quadrature rule.
In this program, We use the stack to implement the Simpson method. Read more about C Programming Language .
Simpson method is used for approximating integral of the function.
Simpson’s rule also corresponds to the 3-point Newton-Cotes quadrature rule.
In this program, We use the stack to implement the Simpson method. Read more about C Programming Language .
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#include<stdio.h>
#include<conio.h>
#include<math.h>
char post_fix[80];
float stack[80];
char stack1[80];
int top=-1,top1=-1;
float eval(char post_fix[], float x1);
void infix_post_fix(char infix[]);
main()
{
float x0, xn, h, s,e1,e2, e3;
char exp[80], arr[80];
int i,n,l=0;
clrscr();
printf("nEnter an expression: nn");
gets(exp);
puts("nnEnter x0, xn and number of sub-intervals: nn");
scanf("%f%f%d", &x0, &xn, &n);
h=(xn-x0)/n;
if(exp[0]=='l'&& exp[1]=='o'&& exp[2]=='g')
{
l=strlen(exp);
for(i=0;i<l-3; i++)
arr[0]=exp[i+3];
arr[i]=";
infix_post_fix(arr);
e1=eval(post_fix,x0);
e2=eval(post_fix,xn);
e3=4*eval(post_fix, x0+h);
s=log(e1)+log(e2)+log(e3);
for (i=3;i<=n-1;i+=2)
s+=4*eval(post_fix,x0+i*h)+2*eval(post_fix, x0+(i-1)*h);
}
else
{
infix_post_fix(exp);
s=eval(post_fix,x0)+eval(post_fix,xn)+4*eval(post_fix, x0+h);
for (i=3;i<=n-1;i+=2)
s+=4*eval(post_fix,x0+i*h)+2*eval(post_fix, x0+(i-1)*h);
}
printf("nnThe value of integral is %6.3fn",(h/3)*s);
return(0);
}
/*Inserting the operands in a stack. */
void push(float item)
{
if(top==99)
{
printf("ntThe stack is full");
getch();
exit(0);
}
else
{
top++;
stack[top]=item;
}
return;
}
/*Removing the operands from a stack. */
float pop()
{
float item;
if(top==-1)
{
printf("ntThe stack is emptynt");
getch();
}
item=stack[top];
top–;
return (item);
}
void push1(char item)
{
if(top1==79)
{
printf("ntThe stack is full");
getch();
exit(0);
}
else
{
top1++;
stack1[top1]=item;
}
return;
}
/*Removing the operands from a stack. */
char pop1()
{
char item;
if(top1==-1)
{
printf("ntThe stack1 is emptynt");
getch();
}
item=stack1[top1];
top1–-;
return (item);
}
/*Converting an infix expression to a postfix expression. */
void infix_post_fix(char infix[])
{
int i=0,j=0,k;
char ch;
char token;
for(i=0;i<79;i++)
post_fix[i]=' ';
push1('?');
i=0;
token=infix[i];
while(token!=")
{
if(isalnum(token))
{
post_fix[j]=token;
j++;
}
else if(token=='(')
{
push1('(');
}
else if(token==')')
{
while(stack1[top1]!='(')
{
ch=pop1();
post_fix[j]=ch;
j++;
}
ch=pop1();
}
else
{
while(ISPriority(stack1[top1])>=ICP(token))
{
ch=pop1();
post_fix[j]=ch;
j++;
}
push1(token);
}
i++;
token=infix[i];
}
while(top1!=0)
{
ch=pop1();
post_fix[j]=ch;
j++;
}
post_fix[j]=";
}
/*Determining the priority of elements that are placed inside the stack. */
int ISPriority(char token)
{
switch(token)
{
case '(':return (0);
case ')':return (9);
case '+':return (7);
case '-':return (7);
case '*':return (8);
case '/':return (8);
case '?':return (0);
default: printf("nnInvalid expression");
}
return 0;
}
/*Determining the priority of elements that are approaching towards the stack. */
int ICP(char token)
{
switch(token)
{
case '(':return (10);
case ')':return (9);
case '+':return (7);
case '-':return (7);
case '*':return (8);
case '/':return (8);
case ":return (0);
default: printf("nnInvalid expression");
}
return 0;
}
/*Calculating the result of expression, which is converted in postfix notation. */
float eval(char p[], float x1)
{
float t1,t2,k,r;
int i=0,l;
l=strlen(p);
while(i<l)
{
if(p[i]==’x')
push(x1);
else
if(isdigit(p[i]))
{
k=p[i]-'0′;
push(k);
}
else
{
t1=pop();
t2=pop();
switch(p[i])
{
case '+':k=t2+t1;
break;
case '-':k=t2-t1;
break;
case '*':k=t2*t1;
break;
case '/':k=t2/t1;
break;
default: printf("ntInvalid expression");
}
push(k);
}
i++;
}
if(top>0)
{
printf("You have entered the operands more than the operatorsnn");
exit(0);
}
else
{
r=pop();
return (r);
}
return 0;
}
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