LIB "finitediff.lib";
list D="Ut","Ux","Uy","U";
list V="t","x","y";
list P="a","b";
setinitials(V,D,P);
matrix M[2][2]=0,-a,-a,0;
list Mat=unitmat(2),M;
list Appr=forward(Ut,U,t),trapezoid(Ux,U,x);
def s=fouriersystem(Mat,Appr);s;
==> [1]:
==>    [1]:
==>       [1]:
==>          _[1,1]=(I*T*Sx+T*Cx)
==>          _[1,2]=0
==>          _[2,1]=0
==>          _[2,2]=(I*T*Sx+T*Cx)
==>       [2]:
==>          _[1,1]=(I*Sx+Cx)
==>          _[1,2]=(2*I*Sx*a*dt+2*Cx*a*dt-2*a*dt)/(dx)
==>          _[2,1]=(2*I*Sx*a*dt+2*Cx*a*dt-2*a*dt)/(dx)
==>          _[2,2]=(I*Sx+Cx)
==>    [2]:
==>       [1]:
==>          _[1]=(I*T*Sx+T*Cx)
==>       [2]:
==>          _[1]=(-2*I*Sx*a*dt+I*Sx*dx-2*Cx*a*dt+Cx*dx+2*a*dt)/(dx)
==>          _[2]=(2*I*Sx*a*dt+I*Sx*dx+2*Cx*a*dt+Cx*dx-2*a*dt)/(dx)
==> [2]:
==>    [1]:
==>       [1]:
==>          (T^2)
==>    [2]:
==>       [1]:
==>          (-8*Cx*a^2*dt^2+4*Cx*a*dt*dx+8*a^2*dt^2-4*a*dt*dx+dx^2)/(dx^2)
==>       [2]:
==>          (-8*Cx*a^2*dt^2-4*Cx*a*dt*dx+8*a^2*dt^2+4*a*dt*dx+dx^2)/(dx^2)