1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple differential eq'n problem, check my answer please!

  1. Sep 20, 2013 #1
    1. The problem statement, all variables and given/known data

    dy/dt=2y+3, y(0)=0.06, find y(1)= ?, Δt=0.1

    2. Relevant equations

    y_k+1 = y_k + Δt*f(t_k, y_k)



    3. The attempt at a solution

    y_1 = y_0 + Δt*f(t_0, y_0)
    y_1 = 0.06 + 0.1*(2(0.06)+3)=0.372

    y(1) = 0.372??
    this doesn't seem right because I did this on excel and i got around a y(1)~4.00. the margin of error seems way to big. help!!
     
  2. jcsd
  3. Sep 20, 2013 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You did the first step of iteration only, and calculated y(0.1). Repeat it nine more times. (But it will be a very poor approximation of y(1).)


    ehild
     
  4. Sep 20, 2013 #3

    is there any way of solving y(1) without doing it nine more times? because my next hw problems has step size 0.01...
     
  5. Sep 21, 2013 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Use a spreadsheet.
     
  6. Sep 21, 2013 #5
    my teacher wants me to compare my approx value with my the spreadsheet value. I was wondering if there was a fast shortcut to calculate by hand y(1) with step sizes like 0.1 or .01? or is the only way to do it is one by one until i reach value y(1)?
     
  7. Sep 21, 2013 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It is easy to solve the differential equation by an exact way. If you consider y as the independent variable, dt/dy = 1/(2y+3). If the derivative of a function f(y) is 1/(2y+3), what is the function?

    t=(1/2) ln|2y+3| + C, y= Ae2t -1.5, with the initial condition, y=1.56e2t -1.5

    ehild
     
  8. Sep 21, 2013 #7
    oooh i actually did do that but I thought I was wrong because my approx value was y(1)=10.0269, which is way different from the excel value of ~4.00. are the error margins usually this big?
     
  9. Sep 21, 2013 #8
    what did you make that A variable equal to?
     
  10. Sep 21, 2013 #9

    ehild

    User Avatar
    Homework Helper
    Gold Member

    I got the same y(1) ≈10. The simple iterative method you applied is quite poor, you have to use very small Δt-s to get near to the real solution. With Δt=0.01 it would be much better. But there are more advanced methods for numerical solution of differential equations, Runge-Kutta method, for example. All of them involve lot of computations, so you need a program to do them.

    ehild
     
    Last edited: Sep 21, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Simple differential eq'n problem, check my answer please!
  1. Please Check My Answer (Replies: 2)

Loading...