Answered: Derive the condition (inequality) in hλ…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Derive the condition (inequality) in hλ that indicates the Region of Absolute Stability for the Trapezoidal Method. You can try to draw this region, but I am only asking for the condition.

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Solution:

The trapezoidal method is a much more accurate method in terms of accuracy, than the Euler method. The equation is given by:

$y_{n + 1} = y_{n} + h / 2 [f (x_{n}, y_{n}) + f (x_{n + 1}, y_{n + 1})], n = 0.1, 2 . . . . . .$

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