MATH215 December 2013
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) •
Question 07 (b)
Consider the following initial value problem for a first-order autonomous ODE:
(b) If , use Euler’s method with step size to approximate the solution at time .
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Euler's method is derived by using a tangent line to a solution curve to approximate the value of the solution a time step h later.
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We have so that if then
We denote y0 = 3/2 and t0 = 0 so that
Continuing in this process,
Notice how this approximated solution slowly approaches the equilibrium value y=1.