Consider the initial-value problem y' = 2y, y(0) = 1. The analytic solution is y = e
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Consider the initial-value problem y' = 2y, y(0) = 1. The analytic solution is y = e2x.
(a) Approximate y(0.1) using one step and Euler’s method.
(b) Find a bound for the local truncation error in y1.
(c) Compare the error in y1 with your error bound.
(d) Approximate y(0.1) using two steps and Euler’s method.
(e) Verify that the global truncation error for Euler’s method is O(h) by comparing the errors in parts (a) and (d).
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Related Book For
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1111827052
10th edition
Authors: Dennis G. Zill
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