Integro-Differential Equation with mathematica

yashar

hi
how can i solve a system of Integro-Differential Equations in mathematica numerically or analytically?
thanks

jackmell

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.