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C++ ::: NUMERICAL ANALYSIS

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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:

			Linear System of Equations
			Non-Linear Equations
			Finite Differences
			Interpolation
			Spline Functions
			Numerical Differentiation
			Numerical Integration
			Ordinary Differential Equations

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


	NA-01		A C++ Program to read a Linear System of Equations, then evaluate it by using Gauss Elimination Method and display the result.
	NA-02		A C++ Program to read a Linear System of Equations, then evaluate it by using LU-Decomposition Method and display the result.
	NA-03		A C++ Program to read a Linear System of Equations, then evaluate it by using Jacobi Iterative Method and display the result.
	NA-04		A C++ Program to read a Linear System of Equations, then evaluate it by using Guass-Seidel Iterative Method and display the result.

Non-Linear Equations


	NA-05		A C++ Program to read a Non-Linear equation in one variable, then evaluate it using Bisection Method and display its kD accurate root.
	NA-06		A C++ Program to read a Non-Linear equation in one variable, then evaluate it using False-Position Method and display its kD accurate root.
	NA-07		A C++ Program to read a Non-Linear equation in one variable, then evaluate it using Modified False-Position Method and display its kD accurate root.
	NA-08		A C++ Program to read a Non-Linear equation in one variable, then evaluate it using Newton-Raphson Method and display its kD accurate root.
	NA-09		A C++ Program to read a Non-Linear equation in one variable, then evaluate it using Secant Method and display its kD accurate root.
	NA-10		A C++ Program to read a Non-Linear equation in one variable, then evaluate it using Simple Itrative Method [ or Fixed-Point Method ] and display its kD accurate root.

Finite Differences


	NA-11		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


	NA-12		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.
	NA-13		A C++ Program to construct and display Divided Difference Table from the given distict data points.
	NA-14		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.
	NA-15		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.
	NA-16		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


	NA-17		A C++ Program to determine whether the given function is a Cubic Spline or not.
	NA-18		A C++ Program to to construct Natural Cubic Spline Interpolant from the given data.
	NA-19		A C++ Program to to construct Clamped Cubic Spline Interpolant from the given data.

Numerical Differentiation


	NA-20		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.
	NA-21		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.
	NA-22		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.
	NA-23		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.
	NA-24		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.
	NA-25		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.
	NA-26		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.
	NA-27		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.
	NA-28		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


	NA-29		A C++ Program to estimate the Integral value of the function at the given point from the given data using Trapezoidal Rule.
	NA-30		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.
	NA-31		A C++ Program to estimate the Integral value of the function at the given point from the given data using Romberg Method.
	NA-32		A C++ Program to to estimate the Integral value of a given function using Gussian Quadrature Rule.

Ordinary Differential Equations


	NA-33		A C++ Program to estimate the Differential value of the function at the given point from the given data using Euler's Method.
	NA-34		A C++ Program to estimate the Differential value of the function at the given point from the given data using Mid-Point Method.
	NA-35		A C++ Program to estimate the Differential value of a given function at given point from given data using Euler-Trapezoidal Rule [ Predictor-Corrector Scheme ].
	NA-36		A C++ Program to estimate the Differential value of a given function at given point from given data using Runge-Kutta Methods.



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