By employing 0-method with 0-0, 0.5, 1, and the step size h=0.2, find the numerical solution of the following problem at t=0.4 Y (t) = te -Y (1), Y (0) = 1. The true solution of this problem is Y (t) = (1+0.5t)e.Compare the errors of the three obtained approximations.

By employing 0-method with 0-0, 0.5, 1, and the step size h=0.2, find the numerical solution of the following problem at t=0.4 Y (t) = te -Y (1), Y (0) = 1. The true solution of this problem is Y (t) = (1+0.5t)e.Compare the errors of the three obtained approximations.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

By employing 0-method with 0-0, 0.5, 1, and the step size h=0.2, find the
numerical solution of the following problem at t=0.4
Y '(t) = te-Y (1),
Y (0) = 1.
The true solution of this problem is Y (t) = (1+0.5t)e.Compare the errors
of the three obtained approximations.

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