Concept explainers
Compute forward and backward difference approximations of
To calculate: The forward and backward difference approximations of
Answer to Problem 1P
Solution:
Forward difference approximation of
Forward difference approximation of
Backward difference approximation of
Backward difference approximation of
Central difference approximation of
Central difference approximation of
Explanation of Solution
Given information:
Function,
Step size,
The initial value of x,
Formula used:
Forward difference approximation of
Forward difference approximation of
Backward difference approximation of
Backward difference approximation of
Central difference approximation of
Central difference approximation of
True percent relative error is,
Calculation:
Consider the function,
First derivation of the function is,
Thus, the true value of the first derivative of
The value of
The value of the function at
The value of
The value of the function at
The value of
The value of the function at
The value of
The value of the function at
The value of
The value of the function at
Forward difference approximation of
For
True percent error is,
Forward difference approximation of
For
True percent error is,
Backward difference approximation of
For
True percent error is,
Backward difference approximation of
For
True percent error is,
Central difference approximation of
For
True percent error is,
Central difference approximation of
For
True percent error is,
Therefore, Forward difference approximation of
Forward difference approximation of
Backward difference approximation of
Backward difference approximation of
Central difference approximation of
Central difference approximation of
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Chapter 23 Solutions
Numerical Methods for Engineers
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