Integro-Differential Equation with mathematica

[yashar]

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

 

[jackmell]

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

By starting off with just one. Say:

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

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

$$\int_0^{x_k} y(t)dt$$

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 $y(x)=2x$. 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.