Concept explainers
To find: the percentage error if Euler’s method with
Answer to Problem 63E
The percentage error is
Explanation of Solution
Given information: Let
Calculation:
To use Euler’s method, make the table as shown below.
(1,3) | 3 | 0.1 | 0.3 | (1.1,3.3) |
(1.1,3.3) | 3.2 | 0.1 | 0.32 | (1.2,3.62) |
(1.2,3.62) | 3.4 | 0.1 | 0.34 | (1.3,3.96) |
(1.3,3.96) | 3.6 | 0.1 | 0.36 | (1.4,4.32) |
By Euler’s method, f (1.4)
To find the exact value of f (1.4) find f ( x) by finding the antiderivative of the differential equation:
Therefore, exact
The percentage error is then:
Therefore, the percentage error is
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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