Central difference approximations to estimate a Jacobian matrxi

I have two functions F(x,y) and G(x,y) defined in script files FM.m and GM.m and I need to use central difference approximations to estimate the Jacobian matrix J=[Fx(1,2) Fy(1,2);Gx(1,2) Gy(1,2)] where Fx,Fy,Gx,Gy denotes partial differentiation variable.

The central difference approximation is f'(x)=(f(x+h)-f(x-h))/2h.

Any help would be really appreciated, thanks!

Answer 1

[Torsten]

J(1,1)=(F(x+h,y)-F(x-h,y))/(2*h);
J(1,2)=(F(x,y+k)-F(x,y-k))/(2*k);
J(2,1)=(G(x+h,y)-G(x-h,y))/(2*h);
J(2,2)=(G(x,y+k)-G(x,y-k))/(2*k);

Best wishes

Torsten.