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Predictor-corrector, starting values with Taylor method

  1. Feb 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi! I need to solve the following ODE:

    [tex]xy'=1-y+x^2y^2, \qquad y(0)=1[/tex]

    using a predictor-corrector method. Starting values need to be found using a Taylor method.
    The exact solution is of the form [tex]\frac{\tan{x}}{x}[/tex]

    2. Relevant equations

    Taylor method of third order (for 1st starting value):

    [tex]y_1=y_0+hy_0'+\frac{h^2}{2}y_o''+\frac{h^3}{6}y_o'''[/tex]

    3. The attempt at a solution
    Right here I bumped into a problem: in order to evaluate the 1st starting value (for example, if I'm using Adams-Bashforth 3rd order as a predictor and Adams-Moulton 3rd order method as a corrector) I get the following:

    [tex]y'=\frac{1}{x}-\frac{y}{x}+xy^2[/tex]

    Dividing with [tex]x=0[/tex] in order to get yields infinity :(. Any help would be appreciated.
     
  2. jcsd
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