need to do flow chart for this method called Backward differ

need to do flow chart for this method called Backward difference expression with error order h

Solution

Taylor series plays a key role in much of classical analysis, the poor reputation
enjoyed by numerical differentiation has led numericalanalysts to construct
techniques for most problems which avoid the explicit use of numerical differentiation.

The differences formula are obtain from the Taylor\'s series expansion for function .

2. See the functions.

3. By given values of in the tables or directly, use the appropriate formula to solve the problem either or with the given and .

4. Differentiate the functions and calculate the actual values for or .

5. Find the absolute error value by subtract the actual value with calculation value (using formula).

Making use of forward difference operator and forward difference table simplifies the
calculations involved in the polynomial approximation of fuctons which are known at equally
spaced data points.
Newton\'s method where the nodel points xi, i = 0, 1, . . . n are equally spaced,
the error is En(x) = (x - x0)(x - x0 - h) . . .(x - x0 - nh) f(n+1)(x) / (n+1)!