The difference splitting scheme for hyperbolic systems with a nonlinear source term
Annotatsiya
In the paper, we propose a systematic approach to design and investigate the adequacyof the computational models for a mixed dissipative boundary value problem posedfor the symmetric t-hyperbolic systems. We consider a two-dimensional linear hyperbolicsystem with variable coefficients including nonlinear source terms in dissipative boundaryconditions. We construct the difference splitting scheme for the numerical calculation ofstable solutions for this system. A discrete analogue of the Lyapunov’s function is constructedfor the numerical verification of stability of solutions for the considered problem.A priori estimate is obtained for the discrete analogue of the Lyapunov’s function. Thisestimate allows us to assert the exponential stability of the numerical solution. A theoremon the exponential stability of the solution of the boundary value problem for linearhyperbolic system and on stability of difference splitting scheme in the Sobolev spaceswas proved. These stability theorems give us the opportunity to prove the convergenceof the numerical solution.