Denote the Euler-method solution of the initial- value problem dx dt x(1) = 1.2 In x using step size h = 0.05 by X(t), and that using h = 0.025 by X(t). Find the values of X (1.5) and

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2.3.4
Denote the Euler-method solution of the initial-
value problem
dx1, x(1)=1.2
dt In x
using step size h = 0.05 by X(t), and that using
h = 0.025 by X(t). Find the values of X₂(1.5) and
X,(1.5). Estimate the error in the value of X,(1.5),
and suggest a value of step size that would provide
a value of X(1.5) accurate to 0.25%. Find the value
of X(1.5) using this step size. Find the exact
solution of the initial-value problem, and determine
the actual magnitude of the errors in X₂(1.5), X,(1.5)
and your final value of X(1.5).
Transcribed Image Text:2.3.4 Denote the Euler-method solution of the initial- value problem dx1, x(1)=1.2 dt In x using step size h = 0.05 by X(t), and that using h = 0.025 by X(t). Find the values of X₂(1.5) and X,(1.5). Estimate the error in the value of X,(1.5), and suggest a value of step size that would provide a value of X(1.5) accurate to 0.25%. Find the value of X(1.5) using this step size. Find the exact solution of the initial-value problem, and determine the actual magnitude of the errors in X₂(1.5), X,(1.5) and your final value of X(1.5).
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