Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation

A few explicit difference schemes are discussed for the numerical solution of the linear hyperbolic equation u"t"t+2@a u"t+@b^2u=u"x"x+f(x,t),@a>0,@b>0, in the region @W={(x,t)|a0} subject to appropriate initial and Dirichlet boundary conditions, where @a and @b are real numbers. The proposed scheme is showed to be unconditionally stable, and numerical result is presented.