This program is made using C as Programming language and Codeblocks as main IDE. Mostly errors will be generated using other IDE such as TurboC or TechApple Devc etc. To Download Codeblocks goto: http:https://www.codeblocks.org/downloads/26 or https://sourceforge.net/projects/codeblocks/files/Binaries/17.12/Windows/codeblocks-17.12mingw-setup.exe/download

and download codeblocks mingw-setup version and install it.

Numerical analysis has numerous applications in all fields of science and some fields of engineering, and essentially any type of work that requires calculations to give very precise solutions.

The point of numerical analysis is to analyze methods that are used to give approximate number solutions to situations where it is unlikely to find the real solution quickly, and to try and improve upon these methods so as to reduce the amount of error generated by computer calculation.

It is essential in work that requires precise numbers to get very good approximations with very little error in them, if approximations with just even 1 or 2% error are used in another calculation, and the answer of that calculation used in another, and so on, the errors will build up and you end up with very unreliable numbers.

This is why it is a good idea to study numerical analysis if you intend to go into any area of work requiring precise calculations, so as to be able to identify if there are areas you can improve so as to better your methods in finding solutions and reducing error.

USEAGES:

• Numerical computing is based on the idea of iterative process.
• Iterative processes involve generation of sequence of approximation with the hope that, the process will end of the required solution.
• Certain methods convert faster than others.
• It is necessary to know that convergence rate of any method to get the required solution.
• Rapid convergent take less execution time.

This program solves the problems regarding:

1. Errors in numerical computation

2. Solution of nonlinear equations
   2.1 Polynomial by Horner's Method
   2.2 Bisection method
   2.3 Newton Raphson method
   2.4 Fixed point iteration method
   2.5 Secant method
   2.6 Horner’s rule

3. Interpolation
   3.1 Finite differences
   3.1.1 Forward differences
   3.1.2 Backward differences
   3.1.3 Central differences
   3.1.4 Symbolic relations
   3.2 Newton’s forward and backward formulae
   3.3 Central differences interpolation formula
   3.3.1 Gauss forward and backward formula
   3.3.2 Stirling’s, Bessel’s and Everett’s formulae
   3.4 Lagrange interpolation
   3.5 Method of least square method (LSM)
   3.5.1 LSM for linear equation (y = a + bx)
   3.5.2 LSM for quadratic equation (y = a + bx + cx2)
   3.5.3 LSM for y = axb
   3.5.4 LSM for y = aebx

4. System of linear equations
   4.1 Solution of linear system – direct method
   4.1.1 Gaussian elimination method
   4.1.2 Gauss Jordan method
   4.1.3 Matrix inversion
   4.2 Solution of linear system – indirect method
   4.2.1 Gauss Jacobi iteration method
   4.2.2 Gauss Seidel iteration method
   4.3 Method of factorization, LU decomposition method
   4.4 Eigen vectors and Eigen values, power method

5. Numerical differentiation and integration
   5.1 Numerical differentiation for 1st and 2nd order differentiation
   5.1.1 Forward formula
   5.1.2 Backward formula
   5.1.3 Central difference formula
   5.2 Numerical integration
   5.2.1 Trapezoidal rule
   5.2.2 Simpson’s 1/3 rule and 3/8 rule
   5.2.3 Romberg integration
   5.2.4 Gaussian integration

6. Numerical solution of ordinary differential equations
   6.1 Euler’s method and modified Euler’s method
   6.2 Rungekutta 2nd order and 4th order methods
   6.3 Boundary value problem (finite difference method)