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Analysis of Forward and Backward Difference Operators in Tabular Functions, Study notes of Mathematical Methods for Numerical Analysis and Optimization

Virtual University of Pakistan (VUP)Mathematical Methods for Numerical Analysis and Optimization

The concepts of forward and backward difference operators in the context of tabular functions. The forward difference operator calculates the functional value difference from the forward value to a given point, while the backward difference operator calculates the functional value difference from the backward value. The mathematical expressions for both operators are provided.

Typology: Study notes

2018/2019

Uploaded on 09/02/2019

muhammad-zohaib-tariq
muhammad-zohaib-tariq 🇵🇰

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Suppose for a given tabular function:
x x1x2 xi1xixi+1 xn1xn
f(x)f(x1)f(x2) f(xi1)f(xi)f(xi+1) f(xn1)f(xn)
Then at given point say xi, the forward di¤erence operator gives the di¤er-
ence of functional values from the forward value to xi.While backward di¤erence
operator at xiis di¤erence from backward value from xi:Mathematically both
are given as:
Forward di¤erence at xi=4(f(xi)) = f(xi+1)f(xi)
Backward di¤erence at xi=r(f(xi)) = f(xi)f(xi1)
1

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Suppose for a given tabular function: x x 1 x 2    xi 1 xi xi+1    xn 1 xn f (x) f (x 1 ) f (x 2 )    f (xi 1 ) f (xi) f (xi+1)    f (xn 1 ) f (xn) Then at given point say xi, the forward di§erence operator gives the di§er- ence of functional values from the forward value to xi.While backward di§erence operator at xi is di§erence from backward value from xi:Mathematically both are given as: Forward di§erence at xi = 4 (f (xi)) = f (xi+1) f (xi) Backward di§erence at xi = r (f (xi)) = f (xi) f (xi 1 )