A difference scheme for Cauchy problem for the hyperbolic equation with self-adjoint operator
A new second order absolutely stable difference scheme is presented for Cauchy problem for second-order hyperbolic differential equations containing the operator A(t). this scheme makes use of this operator which is unbounded linear self-adjoint positive definite with domain in an arbitrary Hilbert space. The stability estimates for the solution of this difference scheme and for the first and second-order difference derivatives are established. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments. (C) 2010 Elsevier Ltd. All rights reserved.
difference scheme stability abstract hyperbolic equation initial-value problem numerical solution