The 2D time-dependent equation is defined over the domain [0,1][0,1] and written as: ut+f(U)x+g(U)y=0 where U=U(x,y,t),f(U)=aU,g(U)=bU,a and b are positive constant. Dirichlet boundary conditions are imposed with: U(x,0,t)=1for0x1andU(0,y,t)=1for0y1. Together with initial data: U(x,y,0)=0.10