11. Consider the initial value problem Y'(t) = a ta-1, Y(0) = 0, %3D %3D where a > 0. The true solution is Y(t) = t". When a integer, the true solu- tion is not infinitely differentiable. In particular, to have Y twice continuously differentiable, we need a > 2. Use the Euler method to solve the initial value problem for a = 2.5, 1.5, 1.1 with stepsize h = 0.2,0.1,0.05. Compute the solution errors at the nodes, and determine numerically the convergence orders of the Euler method for these problems. %3D

11. Consider the initial value problem Y'(t) = a ta-1, Y(0) = 0, %3D %3D where a > 0. The true solution is Y(t) = t". When a integer, the true solu- tion is not infinitely differentiable. In particular, to have Y twice continuously differentiable, we need a > 2. Use the Euler method to solve the initial value problem for a = 2.5, 1.5, 1.1 with stepsize h = 0.2,0.1,0.05. Compute the solution errors at the nodes, and determine numerically the convergence orders of the Euler method for these problems. %3D

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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Concept explainers

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

11. Consider the initial value problem
Y'(t) = a t"-1, Y (0) = 0,
%3D
where a > 0. The true solution is Y(t) = t". When a # integer, the true solu-
tion is not infinitely differentiable. In particular, to have Y twice continuously
differentiable, we need a > 2. Use the Euler method to solve the initial value
problem for a = 2.5, 1.5, 1.1 with stepsize h = 0.2,0.1,0.05. Compute the
solution errors at the nodes, and determine numerically the convergence orders
of the Euler method for these problems.

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