An algorithm of spectrum analysis for symmetric hyperbolic equations

An algorithm for computing eigenspaces of symmetric hyperbolic systems is presented. Such systems emerge in process of solution of many problems (electromagnetism, acoustics, elasticity). For discrete operators the principal invariant subspaces linked with the smallest non-zeroes eigenvalues are computed. They contain an approximation of sufficient smooth eigenfunctions of the original differential operator. The difficulties connected with infinite-dimensional kernel of the differential operator are overcome. The efficiency of the algorithm is demonstrated on the acoustic equations.