Getting Started

After installing the package you can run the first FD script by executing

cd /your/path/to/FD/
xmaple

and then executing the following maple command:

read("fd_first_run.mpl");

which computes the FDA to the following derivatives:

$$ \frac{\partial^2 f(x)}{\partial x^2} $$

$$ \frac{\partial^3 f(t,x,y)}{\partial t \partial x^2} $$

Then by taylor expanding the FDA it confirms that the computed expressions are accurate.

The output of your maple run should look like this:

>	read "FD.mpl":

 

>

MFD():

 

 

Warning, grid_functions is not assigned

FD table updated, see the content using SFDT() command

 

>	grid_functions:={f}:

 

>	expr:=diff(f(x),x,x);

 

 

>	A:=Gen_Sten(expr);

 

>

 

 

>	B := DtoC(A);

 

 

>	B:=convert(series(B,hx),polynom);

 

>

 

 

>	test_resid := simplify(eval(B-expr,{hx=0}));

 

 

Computing df(t,x,y)/dtdx^2 using 2nd order forward in time and 

centered in x scheme: 

 

>	Update_FD_Table(2, table([ t=[0,-1],x=[-1,-1],y=[-1,-1],z=[-1,-1] ]) );

 

>

 

FD table updated, see the content using SFDT() command

 

>	expr:=diff(f(t,x,y),t,x,x);

 

>

 

 

>	A:=Gen_Sten(expr);

 

>

 

 

>	B := DtoC(A);

 

>

 

 

>	stps:=[ht,hx]:

 

>	for ii from 1 to nops(stps) do

 

>	B:=convert(series(B,stps[ii],4),polynom):

 

>

end do:

 

>

B;

 

>

 

 

>	test_resid := simplify(eval(B-expr,{ht=0,hx=0,hy=0}));

 

>

 

 

>

 

The files fd_first_run.mpl and fd_first_run.mw are in the FD's main directory that you downloaded. Feel free to contact Arman Akbarian if you have any trouble starting to use FD.

See the tutorials section for more examples on posing a PDE and solving it using FD.