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Consider the initial-value problem y' = (x + y − 1)2, y(0) = 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5.  At each step compare the approximate value with the actual value of the analytic solution. (Round your answers to four decimal places.)

Consider the initial-value problem y' = (x + y − 1)2, y(0) = 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5.  At each step compare the approximate value with the actual value of the analytic solution. (Round your answers to four decimal places.)

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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Consider the initial-value problem y' = (x + y − 1)2, y(0) = 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5.

 At each step compare the approximate value with the actual value of the analytic solution. (Round your answers to four decimal places.)

Consider the initial-value problem y' = (x + y − 1)², y(0) = 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution. (Round your answers to four decimal places.) h = 0.1 y(0.5)~ y(0.5) h = 0.05 actual value y(0.5) =
Transcribed Image Text:Consider the initial-value problem y' = (x + y − 1)², y(0) = 2. Use the improved Euler's method with h = 0.1 and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution. (Round your answers to four decimal places.) h = 0.1 y(0.5)~ y(0.5) h = 0.05 actual value y(0.5) =
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