Denote the Euler-method solution of the initial- value problem dx 1 dt xt = x(1) = 1 using step size h = 0.1 by X(t), and that using h = 0.05 by X(t). Find the values of X,(2) and X(2). Estimate the error in the value of X,(2), and suggest a value of step size that would provide a value of X(2) accurate to 0.2%. Find the value of X(2) using this step size. Find the exact solution of the initial-value problem, and determine the actual magnitude of the errors in X₂(2), X,(2) and your final value of X(2).
Denote the Euler-method solution of the initial- value problem dx 1 dt xt = x(1) = 1 using step size h = 0.1 by X(t), and that using h = 0.05 by X(t). Find the values of X,(2) and X(2). Estimate the error in the value of X,(2), and suggest a value of step size that would provide a value of X(2) accurate to 0.2%. Find the value of X(2) using this step size. Find the exact solution of the initial-value problem, and determine the actual magnitude of the errors in X₂(2), X,(2) and your final value of X(2).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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![2.3.4
Denote the Euler-method solution of the initial-
value problem
dx
1
x(1) = 1
dt xt
using step size h = 0.1 by X(t), and that using
h = 0.05 by X(t). Find the values of X₂ (2) and
X(2). Estimate the error in the value of X₁(2), and
suggest a value of step size that would provide a
value of X(2) accurate to 0.2%. Find the value of
X(2) using this step size. Find the exact solution of
the initial-value problem, and determine the actual
magnitude of the errors in X₂(2), X, (2) and your
final value of X(2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75fdb37c-adc4-4f09-9ed1-9117a89a9487%2Fdc14974b-f15b-48d8-8ca4-5b19426b2a37%2Fhyzq9wg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.3.4
Denote the Euler-method solution of the initial-
value problem
dx
1
x(1) = 1
dt xt
using step size h = 0.1 by X(t), and that using
h = 0.05 by X(t). Find the values of X₂ (2) and
X(2). Estimate the error in the value of X₁(2), and
suggest a value of step size that would provide a
value of X(2) accurate to 0.2%. Find the value of
X(2) using this step size. Find the exact solution of
the initial-value problem, and determine the actual
magnitude of the errors in X₂(2), X, (2) and your
final value of X(2).
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