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Solution of Helmholtz equation with impedance boundary condition on finiteinterval is equivalently reformulated as steady state of initial boundary valueproblem for first order hyperbolic system of partial differential equations.Particularly interesting property of the proposed hyperbolic model is thatsteady state is achieved in finite time. For large wavenumber the numericallychallenging task for Helmholtz equation is achieving high accuracy with smallnumber of nodal points. We successfully solved this problem by means of usingwell balanced scheme approach. Numerical tests demonstrate excellentcomputational potential of the proposed method: high accuracy is achieved forlarge wavenumber with small number of nodal points in space and time.

Hyperbolic model for Helmholtz equation with impedance boundary conditions