



C++ ::: NUMERICAL ANALYSIS 


The process of obtaining a solution is to reduce the original problem to a repetition of the same step or series of steps so that the computations become automatic. Such a process is called a Numerical Method and the derivation and analysis of such methods lie within the discipline of Numerical Analysis . Thus, the subject of numerical analysis is concerned with the derivation, analysis and implementation of methods for obtaining reliable numerical answers to complex mathematical problems. In other words, numerical Analysis is the subject concerned with the construction, analysis, and use of algorithms for the numerical solution of mathematical problems to given degree of numerical accuracy.
Select one of the Topics listed below:

Note: All the given files are in zip format, which can be uncompressed with the help of a compression tool. If you do not have any tool, then you can get one from Utilities : Compression Tools. 


Linear System of Equations 






NA01 

A C++ Program to read a Linear System of Equations, then evaluate it by using Gauss Elimination Method and display the result. 
NA02 

A C++ Program to read a Linear System of Equations, then evaluate it by using LUDecomposition Method and display the result. 
NA03 

A C++ Program to read a Linear System of Equations, then evaluate it by using Jacobi Iterative Method and display the result. 
NA04 

A C++ Program to read a Linear System of Equations, then evaluate it by using GuassSeidel Iterative Method and display the result. 





NonLinear Equations 






NA05 

A C++ Program to read a NonLinear equation in one variable, then evaluate it using Bisection Method and display its kD accurate root. 
NA06 

A C++ Program to read a NonLinear equation in one variable, then evaluate it using FalsePosition Method and display its kD accurate root. 
NA07 

A C++ Program to read a NonLinear equation in one variable, then evaluate it using Modified FalsePosition Method and display its kD accurate root. 
NA08 

A C++ Program to read a NonLinear equation in one variable, then evaluate it using NewtonRaphson Method and display its kD accurate root. 
NA09 

A C++ Program to read a NonLinear equation in one variable, then evaluate it using Secant Method and display its kD accurate root. 
NA10 

A C++ Program to read a NonLinear equation in one variable, then evaluate it using Simple Itrative Method [ or FixedPoint Method ] and display its kD accurate root. 





Finite Differences 






NA11 

A C++ Program to read a Non Linear Function [ or function values at different points ], then construct and display the Difference Table. Also read Difference Operators [ Shift, Forward and Backward Operators ], compute and diplay their values. 





Interpolation 






NA12 

A C++ Program to construct Lagranges's Formula from the given distinct data points and estimate the value of the function at the given points. 
NA13 

A C++ Program to construct and display Divided Difference Table from the given distict data points. 
NA14 

A C++ Program to construct Newton's Divided Difference Interpolation Formula from the given distict data points and estimate the value of the function at the given points. 
NA15 

A C++ Program to construct Newton's Forward Difference Interpolation Formula from the given distict equally spaced data points and estimate the value of the function at the given points. 
NA16 

A C++ Program to construct Newton's Backward Difference Interpolation Formula from the given distict equally spaced data points and estimate the value of the function at the given points. 





Spline Functions 






NA17 

A C++ Program to determine whether the given function is a Cubic Spline or not. 
NA18 

A C++ Program to to construct Natural Cubic Spline Interpolant from the given data. 
NA19 

A C++ Program to to construct Clamped Cubic Spline Interpolant from the given data. 





Numerical Differentiation 






NA20 

A C++ Program to estimate the value of First Derivative of the function at the given points from the given data using Backward Difference Formula and Forward Difference Formula of Order One. 
NA21 

A C++ Program to estimate the value of First Derivative of the function at the given points from the given data using Central Difference Formula of Order Two. 
NA22 

A C++ Program to estimate the value of First Derivative of the function at the given points from the given data using Central Difference Formula of Order Four. 
NA23 

A C++ Program to estimate the value of Second Derivative of the function at the given points from the given data using Central Difference Formula of Order Two. 
NA24 

A C++ Program to estimate the value of Second Derivative of the function at the given points from the given data using Central Difference Formula of Order Four. 
NA25 

A C++ 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 Two. 
NA26 

A C++ 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 Four. 
NA27 

A C++ Program to estimate the value of Fourth Derivative of the function at the given points from the given data using Central Difference Formula of Order Two. 
NA28 

A C++ Program to estimate the value of Fourth Derivative of the function at the given points from the given data using Central Difference Formula of Order Four. 





Numerical Integration 






NA29 

A C++ Program to estimate the Integral value of the function at the given point from the given data using Trapezoidal Rule. 
NA30 

A C++ Program to estimate the Integral value of the function at the given point from the given data using Simpson's 1/3 Rule. 
NA31 

A C++ Program to estimate the Integral value of the function at the given point from the given data using Romberg Method. 
NA32 

A C++ Program to to estimate the Integral value of a given function using Gussian Quadrature Rule. 





Ordinary Differential Equations 






NA33 

A C++ Program to estimate the Differential value of the function at the given point from the given data using Euler's Method. 
NA34 

A C++ Program to estimate the Differential value of the function at the given point from the given data using MidPoint Method. 
NA35 

A C++ Program to estimate the Differential value of a given function at given point from given data using EulerTrapezoidal Rule [ PredictorCorrector Scheme ]. 
NA36 

A C++ Program to estimate the Differential value of a given function at given point from given data using RungeKutta Methods. 




