(e) Consider the initial value problem y = y - 2, y (0) = 4 Do two steps of Euler's method with each of the following step sizes: h= 1, h = 2, h = 1/2. Compare these results to a stability analysis of equilibrium solutions for the differential equation, and discuss the consequences of approximating with these different step sizes.
(e) Consider the initial value problem y = y - 2, y (0) = 4 Do two steps of Euler's method with each of the following step sizes: h= 1, h = 2, h = 1/2. Compare these results to a stability analysis of equilibrium solutions for the differential equation, and discuss the consequences of approximating with these different step sizes.
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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Solve letter (e) for Eulers Method
Transcribed Image Text:(d) Use Euler's Method with step size h = 2 to approximate y(8) for the function y(t) that
is a solution to the initial value problem
(e) Consider the initial value problem
y' = 4y,
3. Integration review
y' =y-2,
y(0) = 4
Do two steps of Euler's method with each of the following step sizes: h= 1, h = 2,
h = 1/2. Compare these results to a stability analysis of equilibrium solutions for the
differential equation, and discuss the consequences of approximating with these different
step sizes.
y (0) = 0
fr²e dr
• fcos(x) sin(sin(x)) dr
(a) Evaluate the following indefinite integrals. In each case, the first step will be to analyze
the integral and select the appropriate technique(s).
• S=
x²-3x-15
6
Si de
dx
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