FINITE DIFFERENCES

Finite difference method is used for complex differential equations which are difficult to solve by any methods. Finite difference is an approximation method. There are different functions or applications for finite difference method.

1. Polynomial determination for curve fitting
2. Interpolation
3. Differentiation and Integration
4. Smoothing of data

The methods for each of these applications usually introduce a formula with a certain pattern which could be used after iteration. The iteration process is taking differences between data.

POLYNOMIAL FUNCTION

The number of iteration is taken as the degree of polynomial. If there are 3 iteration steps for constant difference then the formula is:

                          

The leading coefficient being a.

INTERPOLATION FUNCTION

There are different methods for solving interpolation using finite difference with difference equation patterns.

1. Gregory-Newton Forward Interpolation Method
2. Gregory-Newton Backward Interpolation Method
3. Gregory-Newton Divided Interpolation Method
4. Lagrange Interpolation Method
5. Stirling Formula in Forward Difference
6. Gauss's Forward Interpolation Formula
7. Gauss's Backward Interpolation Formula

DIFFERENTIATION AND INTEGRATION FUNCTION

In using finite difference in solving for complex derivatives, three major methods are used:

1. Backward difference
2. Forward difference
3. Central difference

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