Home | | Business Maths 12th Std | Finite Differences: Solved Example Problems

Numerical Methods - Finite Differences: Solved Example Problems | 12th Business Maths and Statistics : Chapter 5 : Numerical Methods

Chapter: 12th Business Maths and Statistics : Chapter 5 : Numerical Methods

Finite Differences: Solved Example Problems

Numerical Methods: Finite Differences: Solved Example Problems

Example 5.1

Construct a forward difference table for the following data


Solution:

The Forward difference table is given below


 

Example 5.2

Construct a forward difference table for y = f(x) = x 3 + 2x + 1 for x = 1,2,3,4,5

Solution:

y = f(x) = x3 + 2 x + 1 for x =1,2,3,4,5


 

Example 5.3

By constructing a difference table and using the second order differences as constant, find the sixth term of the series 8,12,19,29,42…

Solution:

Let k be the sixth term of the series in the difference table

First we find the forward differences.


Given that the second differences are constant

k – 55 = 3

 k = 58

the sixth term of the series is 58

 

Example 5.4

Find (i) ∆eax (ii) ∆2ex  (iii) ∆logx

Solution:


 

Example 5.5

Evaluate  by taking ‘1’ as the interval of differencing.

Solution:


 

Example 5.5

Evaluate  by taking ‘1’ as the interval of differencing.

Solution:


 

Example 5.7

Prove that f(4) = f(3) + Δf(2) + Δ2f(1) + Δ3f(1) taking ‘1’ as the interval of differencing.

Solution:

We know that f(4) - f(3) = Δ f(4)

f(4) - f(3) = Δ f(3)

= Δ [ f(2) + Δf(2) ]    i.e.[ f(3) - f(2) = Δf(2) ]

= Δ f(2) + Δ2f(2)

= Δ f(2) + Δ2[f(1)+ Δf(1)]

f(4) = f(3) + Δf(2) + Δ2 f(1) + Δ3 f(1)

 

Example 5.8

Given U0 =1, U1 =11, U2 =21, U3 =28 and U4 =29 find Δ4U0

Solution:

Δ4U0 = (E-1) 4U0


 

 


Tags : Numerical Methods , 12th Business Maths and Statistics : Chapter 5 : Numerical Methods
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
12th Business Maths and Statistics : Chapter 5 : Numerical Methods : Finite Differences: Solved Example Problems | Numerical Methods


Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.