Consider the initial value problem • y'=x^2 + y^2, y(0) = 1. • step size of h=0.02 • 10 iterations Using the third-order Taylor method, solve for the following: • approximate the value of y(0.2) with 6 decimal places • the value after iteration 5 with 6 decimal places • the value after iteration 8 with 6 decimal places Iteration 5 Approximation Iteration 8 ✓ [Choose ] 1.063904 1.111463 1.253016 1.286129 1.191976 1.221679

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the initial value problem
• y'=x^2 + y^2, y(0) = 1.
• step size of h=0.02
• 10 iterations
Using the third-order Taylor method, solve for the following:
• approximate the value of y(0.2) with 6 decimal places
• the value after iteration 5 with 6 decimal places
• the value after iteration 8 with 6 decimal places
Iteration 5
Approximation
Iteration 8
✓ [Choose ]
1.063904
1.111463
1.253016
1.286129
1.191976
1.221679
Transcribed Image Text:Consider the initial value problem • y'=x^2 + y^2, y(0) = 1. • step size of h=0.02 • 10 iterations Using the third-order Taylor method, solve for the following: • approximate the value of y(0.2) with 6 decimal places • the value after iteration 5 with 6 decimal places • the value after iteration 8 with 6 decimal places Iteration 5 Approximation Iteration 8 ✓ [Choose ] 1.063904 1.111463 1.253016 1.286129 1.191976 1.221679
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