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Euler's Method Question?
(a) Use Euler's method with step size 0.1 to estimate y(1.4), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places.
y' = x - xy
y(1) = 0
My work:
y(1) = 0
->y'(1) = 1 - 1 * 0 = 1
y(1.1) = y(1) + .1 * y'(1) = 0 + .1 * 1 = .1
-> y'(1.1) = 1.1 - 1.1 * .1 = .99
y(1.2) = y(1.1) + .1 * y'(1.1) = .1 + .1 * .99 = .199
-> y'(1.2) = 1.2 - 1.2 * .199 = .9612
y(1.3) = y(1.2) + .1 * y'(1.2) = .199 + .1 * .9612 = .29512
-> y'(1.3) = 1.3 - 1.3 * .29512 = .916344
y(1.4) = y(1.3) + .1 * y'(1.3) = .29612 + .1 * .916344 = .3877544 or in 4 decimal places .3878 ... this is not correct. The previous problem was the same question, except I was supposed to use step size of .2, and I got .392 (and it was correct), so I don't know what the problem is.
Thanks!
1 Answer
- 8 years ago
I always find it easier to make a chart with this types of problems.
Make it look like this:
X Y DX DY NEW X NEW Y
make sure you solve for dy, first. your first x would be 1 in this case, with a y of 0. Your change in x (dx) would be .1, which is given in the question. Plug those three values into into the differential equation to find the dy. Now that you have your dx and dy, you just add that to your x and y to find your new x and new y.
Do this until your new x is 1.4, then the new y that comes with that is your answer.
