The Complete Codes

C program for Simpson's 1/3 Rule  Before Starting the program let us know about the Simpson's 1/3 rule and How it works? Simpson’s 1/3 Rule The trapezoidal rule was based on approximating the integrand by a first-order polynomial and then integrating the polynomial over an interval of integration. Simpson’s 1/3 rule is an extension of the Trapezoidal rule where the integrand is approximated by a second-order polynomial.

C programming to calculate value using composite trapezoidal rule #include<stdio.h> #include<conio.h> #include<math.h> #define F(x) 2*x int main() { int n,i; float a,b,h,x,sum=0,integral; printf("Enter the two limits:\n"); scanf("%f%f",&a,&b); printf("Enter the difference n:\n"); scanf("%d",&n); h=(b-a)/n; for(i=1;i<n;i++) { x=a+i*h; sum=sum+F(x); } integral=(h/2)*(F(a)+F(b)+2*sum); printf("\nThe integral is: %f\n",integral); return 0; }

C Programming Codes To Compute Value Using Trapezoidal Rule #include<stdio.h> #include<conio.h> #include<math.h> #define F(x) exp(-(x/2)) int main() { int a,b,h; float i,x,y; printf("Enter the value for lower and upper limit\n"); scanf("%d%d",&a,&b); h=b-a;//Calculating height x=F(a);//Calculation Function and storing in x and y. y=F(b); i=h*((x+y)/2); printf("The Intregrated Value is %.3f",i); }

C Program To Calculate Values Using Fixed Point Iteration Method Algorithm Start Read values of x0 and e. *Here x0 is the initial approximation e is the absolute error or the desired degree of accuracy, also the stopping criteria* Calculate x1 = g(x0) If [x1 – x0] <= e, goto step 6. *Here [ ] refers to the modulus sign* Else, assign x0 = x1 and goto step 3. Display x1 as the root. Stop #include<stdio.h> #include<math.h> #include<conio.h> #define EST 0.05 #define F(x) exp(-x)-x #define G(x) exp(-x) int main() { int i=1; float error,x0,x1,temp; printf("Enter the initial guess x0:\n"); scanf("%f",&x0); printf("Iteration x0\t\t x1\t Error\n"); x1=G(x0); error=fabs((x1-x0)/x1); printf("%d\t %.4f\t%.4f\t %.4f\n",i,x0,x1,error); do { i++; temp=x1; x0=temp; x1=G(x0); error=fabs((x1-x0)/x1); printf("%d\t %.4f\t%.4f\t %.4f\n",i,x0,x1,error); }while (error>EST); } C Program To Calculate Values Using Ho

C program to find value using Bisection Method | C Programming #include<stdio.h> #include<conio.h> #include<math.h> #define EST 0.05 #define F(x) pow(x,3)-x-3 int main() { int i=1; float xl,xu,xm,f1,f2,f3,error; printf("Enter the values for xl and xu respectively\n"); scanf("%f%f",&xl,&xu); printf("Iteration\tXl\t Xu\t f(Xm)\t Error\n"); do { xm=(xl+xu)/2; f1=F(xl); f2=F(xu); f3=F(xm); error=fabs((xl-xu)/xu); if((f1*f3)<0) { xu=xm; } else { xl=xm; } f3=F(xm); error=fabs((xl-xu)/xu); printf("%d\t %.4f\t %.4f\t%.4f\t %.4f\n",i,xl,xu,xm,error); i++; }while (error>=EST); }

C program to find value using secant method | C programming #include<stdio.h> #include <math.h> #include<conio.h> #define EST 0.05 #define F(x) x-exp(x)+2 int main() { int i = 1; float x0,x1,a,b,c,d,f1,x2,f0,error; printf("\nEnter the value of x0: "); scanf("%f",&x0); printf("\nEnter the value of x1: "); scanf("%f",&x1); printf("\n__________________________________________________________________\n"); printf("\niteration\tx0\t x1\t f0\t f1\t x2\t\terror"); printf("\n___________________________________________________________________\n"); f0=F(x0); f1=F(x1); x2=x1-((f1*(x1-x0))/(f1-f0)); printf("%f",x2); error=fabs((x2-x1)/x2); printf("\n %d \t %.2f\t %.2f\t %.2f \t %.3f \t %.3f \t %.3f", i, x0,x1,f0,f1,x2,error); do{ i++; x0=x1; f0= f1; x1=x2; f0=F(x0); f1=F(x1); x2=x1-((f1*(x1-x0))/(f1-f0)); error=fabs((x2-x1)/x2); printf("\n %d \t %.2f\t %.2f\t %.2f \t %.4f \

C program to find the value using Newton Raphson Before starting with the program let us learn something about Newton Raphson Method Newton Raphson Method  is open method and starts with one initial guess for finding real root of non-linear equations. In other Words,  Newton Raphson method, also called the Newton’s method, is the fastest and simplest approach of all methods to find the real root of a nonlinear function. It is an open bracket approach, requiring only one initial guess. This method is quite often used to improve the results obtained from other iterative approaches