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Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's explicit method. with h=0.4. The analytical solution of the ODE is: y = x + Ze-x-1.In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.

Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's explicit method. with h=0.4. The analytical solution of the ODE is: y = x + Ze-x-1.In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.

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 following first-order ODE: x-y from x0 tox 1.2 with y(0) - 1 dz Solve using Kuler's explicit method.with h = 0.4. The analytical solution of the ODE is: y=x+2e-1. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. X 0 0.4 0.8 1.2 1 0.4 0.52 0.928 error 0 0.2976 0.2824 0.202 X 0 0.4 0.8 1.2 y 1 0.5 0.5 0.75 error 0 0.2131 0.2358 0.196 X 0 0.4 0.8 1.2 y 1 0.6 0.52 0.632 error 0 0.1406 0.1787 0.170 None of the choices
Transcribed Image Text:Consider the following first-order ODE: x-y from x0 tox 1.2 with y(0) - 1 dz Solve using Kuler's explicit method.with h = 0.4. The analytical solution of the ODE is: y=x+2e-1. In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined. X 0 0.4 0.8 1.2 1 0.4 0.52 0.928 error 0 0.2976 0.2824 0.202 X 0 0.4 0.8 1.2 y 1 0.5 0.5 0.75 error 0 0.2131 0.2358 0.196 X 0 0.4 0.8 1.2 y 1 0.6 0.52 0.632 error 0 0.1406 0.1787 0.170 None of the choices
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