a b s t r a c tIn this note, Finite Element Method is applied to solve the symmetric t-hyperbolic system with dissipative boundary condition and its stability is proved. In two-dimensional space, complex program is developed for the numerical solution of the mixed problem in simple connected region on the uniform grid. Delphi-7 is used for the code of the complex program. Numerical results are in line with the theoretical findings. R.D. Aloev et al. / Computers and Mathematics with Applications ( ) -R.D. Aloev et al. / Computers and Mathematics with Applications ( ) -