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1- Apply the backward Euler method to solve the initial value problem Consider the initial value problem Y'(t)=a t^a - 1, Y(0)=-0, where a > 0. The true solution is Y(t) = t^a . The true solution is not infinitely differentiable when a { is not equal} integer. 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 step size 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.

1- Apply the backward Euler method to solve the initial value problem Consider the initial value problem Y'(t)=a t^a - 1, Y(0)=-0, where a > 0. The true solution is Y(t) = t^a . The true solution is not infinitely differentiable when a { is not equal} integer. 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 step size 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.

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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1- Apply the backward Euler method to solve the initial value problem Consider the initial value problem Y'(t)=a t^a - 1, Y(0)=0, where a > 0. The true solution is Y(t) = t^a . The true solution is not infinitely differentiable when a { is not equal} integer. 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 step size 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.
Transcribed Image Text:1- Apply the backward Euler method to solve the initial value problem Consider the initial value problem Y'(t)=a t^a - 1, Y(0)=0, where a > 0. The true solution is Y(t) = t^a . The true solution is not infinitely differentiable when a { is not equal} integer. 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 step size 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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