Results 1 to 3 of 3

Math Help - numerical solution to differencial equation

  1. #1
    Newbie
    Joined
    Dec 2006
    Posts
    9

    numerical solution to differencial equation

    dy/dx = y' = f(x,y(x)) = 2e^(-x^2)

    Solve this differential equation using Heun's method and plot solution over -5 < x < 5. You'll need to derive the appropriate initial condition y(x0) = y0

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 12_bladez View Post
    dy/dx = y' = f(x,y(x)) = 2e^(-x^2)

    Solve this differential equation using Heun's method and plot solution over -5 < x < 5. You'll need to derive the appropriate initial condition y(x0) = y0

    Heun's method is the basic Predictor Corrector method. This uses the Euler
    step to predict the value of y(x+h) using y(x) and y'(x). Then using the
    prediction of y(x+h) calculate the derivative y'(x+h), then a new estimate
    of the derivative over the interval is taken as the average of the two
    derivatives found and y(x+h) is then found using an Euler step with this
    new estimate of the derivative.

    Here f(x,y(x)) is independent of y so that makes things a bit simpler, since
    now we can calculate y'(x+h) without having to estimate y(x+h). So in
    this case the Heun step is:

    y(x+h) = y(x) + h [y'(x) + y'(x+h)]/2

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by 12_bladez View Post
    dy/dx = y' = f(x,y(x)) = 2e^(-x^2)

    Solve this differential equation using Heun's method and plot solution over -5 < x < 5. You'll need to derive the appropriate initial condition y(x0) = y0

    Quote Originally Posted by CaptainBlack View Post
    Heun's method is the basic Predictor Corrector method. This uses the Euler
    step to predict the value of y(x+h) using y(x) and y'(x). Then using the
    prediction of y(x+h) calculate the derivative y'(x+h), then a new estimate
    of the derivative over the interval is taken as the average of the two
    derivatives found and y(x+h) is then found using an Euler step with this
    new estimate of the derivative.

    Here f(x,y(x)) is independent of y so that makes things a bit simpler, since
    now we can calculate y'(x+h) without having to estimate y(x+h). So in
    this case the Heun step is:

    y(x+h) = y(x) + h [y'(x) + y'(x+h)]/2

    RonL
    So now we can do the integration, lets assume the initial condition is y(-5)=0.

    A table showing the calculation is shown in the attachment.

    RonL
    Attached Thumbnails Attached Thumbnails numerical solution to differencial equation-gash.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 29th 2011, 03:59 PM
  2. Help with numerical solution of PDE
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: March 20th 2010, 01:37 PM
  3. Replies: 1
    Last Post: October 18th 2008, 04:55 AM
  4. numerical solution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 7th 2008, 04:30 AM
  5. Replies: 1
    Last Post: October 1st 2006, 07:40 AM

Search Tags


/mathhelpforum @mathhelpforum