Results 1 to 7 of 7

Math Help - Linearization of nonlinear equations with approximation

  1. #1
    Newbie
    Joined
    May 2011
    From
    Ahwaz, Iran
    Posts
    4

    Linearization of nonlinear equations with approximation

    Dear friends,

    Can anybody help me to make an approximation to a nonlinear equation like (x-y)^0.5 in terms of x and y?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Use the Taylor formula

    f(x,y)\;\approx \;f(x_0,y_0)+\dfrac{\partial f}{\partial x}(x_0,y_0)\;(x-x_0)+\dfrac{\partial f}{\partial y}(x_0,y_0)\;(y-y_0)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2011
    From
    Ahwaz, Iran
    Posts
    4
    Thanks for your comment. Indeed, I need a parametric function in terms of x and y like what is written for (x-y)^2=x^2+y^2-2xy. However, I know there is not an exact extension for my equation. I think there is maybe a simplified form with a reasonable approximation.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,306
    Thanks
    1282
    Yes, an approximation is what you asked for and what FernandoRevilla gave you. Your function is f(x,y)= (x- y)^{0.5}, so its first order partial derivatives are f_x= (0.5)(x- y)^{-0.5} and f_y= -(0.5)(x- y)^{-0.5}. Evaluate those at some (x_0, y_0) and put into FernandoRevilla's formula. Of course, any approximation is not going to be equally accurate for all x and y. You need to decide where you want the approximation to be most accurate and pick x_0 and y_0 there.
    Last edited by HallsofIvy; May 6th 2011 at 04:57 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2011
    From
    Ahwaz, Iran
    Posts
    4
    Thank u HallsofIvy, I got your point. I will check it in my problem. Defining x0 and y0 is the central challenge here.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ali1980 View Post
    Thank u HallsofIvy, I got your point. I will check it in my problem. Defining x0 and y0 is the central challenge here.
    There is another approach which minimises some function of the error in the linear approximation across some region of the x-y plane but from what you write I guess that would be beyond you at present.

    CB
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2011
    From
    Ahwaz, Iran
    Posts
    4
    Thanks CaptainBlack, maybe an iterative solution can minimize the errors. But if you know a better approach, please let me know.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. System of nonlinear equations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 7th 2010, 05:19 AM
  2. System of nonlinear equations
    Posted in the Math Software Forum
    Replies: 2
    Last Post: June 11th 2010, 06:29 AM
  3. help on linearization / linear approximation
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 29th 2009, 01:22 PM
  4. Help with nonlinear differntial equations !!!
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: May 25th 2009, 04:04 PM
  5. Nonlinear Systems of Equations
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 20th 2008, 12:55 PM

Search Tags


/mathhelpforum @mathhelpforum