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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).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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).
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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