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A difference scheme for Cauchy problem for the hyperbolic equation with self-adjoint operator. (English) Zbl 1201.65150

Summary: 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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