Answered: 12. The solution of Y'(t) = XY(t) +…

12. The solution of Y'(t) = XY(t) + cos(t) – A sin(t), Y(0) = 0 %3D is Y (t) = sin(t). Find the asymptotic error formula (2.36) in this case. Also compute the Euler solution for 0

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

12. The solution of
Y'(t) = XY (t) + cos(t) – A sin(t), Y(0) = 0
is Y (t) = sin(t). Find the asymptotic error formula (2.36) in this case. Also
compute the Euler solution for 0 <t < 6, h = 0.2,0.1,0.05, and A = 1, –1.
Compare the true errors with those obtained from the asymptotic estimate
%3D
Y (tn) – Yn z hD(tn).

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