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Integro-Differential Equation with mathematica

  1. Dec 30, 2011 #1
    hi
    how can i solve a system of Integro-Differential Equations in mathematica numerically or analytically?
    thanks
     
  2. jcsd
  3. Dec 31, 2011 #2
    By starting off with just one. Say:

    [tex]y'(x)=2-1/4 x^2+1/4\int_0^x y(t)dt,\quad y(0)=0[/tex]

    Now, modify for example the Euler method so that at evey time step, compute the developing integral for example at time step [itex]x_k[/itex], compute (numerically)

    [tex]\int_0^{x_k} y(t)dt[/tex]

    where the values of y(t) are obtained from the previous calculations. Then just add that part to the regular calculations for that method. Try to write a Mathematica program to implement this and see if you come out with [itex]y(x)=2x[/itex]. Get that perfected, then move on to more complicated ones. There are no built-in commands to compute IDEs in Mathematica although I'm sure the Mathematica community has written some numerical ones.
     
    Last edited: Dec 31, 2011
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