a) Derive a suitable numerical differentiation formula of to find
with
given the table
| x | 0.1 | 1.2 | 2.4 | 3.9 |
| f(x) | 3.41 | 2.68 | 1.37 | -1.48 |
To numerically differentiate and find \( f''(2.4) \) using the given table, we will use a suitable numerical differentiation formula of order \( O(h^2) \). Given: - \( h = 0.1 \) - Table of values: | \( x \) | 0.1 | 1.2 | 2.4 | 3.9 | |---------|------|------|------|------| | \( f(x) \) | 3.41 | 2.68 | 1.37 | -1.48 | ### Step 1: Numerical Differentiation Formula For a second derivative approximation \( f''(x) \), we ____ _______ ________ ______ ___ _____.
_________ ____ _________ _______ ___ _______ ________ _________ _____ _________.
_____ __________ ______ ____ __________ ______ ______.
______ _______ ______ ___ _________ _________ ___ _____ _____.
______ _________ ________ _______ _____.
___ _________ ________ _____ _________ _________.
_______ _____ _____ _________ __________ ____ _______.
__________ _____ ________ ______ ______ __________ __________ ______ ____.
_______ _____ ________ ________ _________ ________ _________ ___ _____ ________ ______ ____.
______ ______ __________ _____ ____ _________ ________ ______ _________ ______ __________ _______.
__________ ___ ___ ___ __________ _________ _______.
_______ __________ _____ ________ ______ ___ ____ _________ _______.
_____ ____ ______ ______ _____.
___ _____ ______ ________ ___ ___ ___ ________ _________ ________.
______ ____ _____ ________ _______.
_____ ________ _______ _____ _____ ____ ___ ______ ___.
_______ ______ ______ ___ ___ ____ ____ ____.
____ ___ ___ ____ _____ ________ _______.
_______ ___ _______ _______ ________ ________ _______ _______.
__________ ___ __________ ____ ____ _________ _____.
____ ________ ____ ___ ________ _______ ________ __________ _____ _________.
________ _________ _______ _________ ____ _______.
___ ____ ________ ___ ______ _____ _______ _________ ____.
___ __________ ______ _______ _____ ___ __________ ______ _____ _________.
_____ ____ ________ ____ _____ ___ ______ _____ _____.
_______ _____ ____ _______ ___ ______ _______.
______ _______ _________ ___ ______ ___ ______ ___ _______ __________ ______ ____.
______ ____ __________ ______ _______ _____ _________ _______ __________ ___.
__________ _____ ___ ___.
Get Full Answer on WhatsApp
b) Use modified Euler’s method to find the approximate solution of IVP
at
with
If the exact solution is find the error.
b) A table of values is to be constructed for the function given by
in the interval [1, 4] with equal step length. Determine the spacing h such that quadratic interpolation gives result with accuracy
c) Show that is a solution of the difference equation
b) The function is to be tabulated at equispaced points in the interval [2, 3] using linear interpolation. Find the largest step size h that can be used so that the error
in magnitude.
c) Solve for the root lying between 2 and 4 by the method of false position. Perform two iterations
c) Find the inverse of the matrix
using Gauss Jordan method.
b) Find by Newton’s method the roots of the following equations correct to three places of decimals
i) near
ii)