## A note on the difference schemes for hyperbolic equations.(English)Zbl 1007.65064

The authors present some methods discrete in time for the hyperbolic equation $$d^2 u(t)/dt^2+ Au(t)= f(t)$$, $$u(0)= \phi$$, $$u'(0)= \psi$$ in Hilbert space and find stability estimates.

### MSC:

 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L15 Initial value problems for second-order hyperbolic equations 34G10 Linear differential equations in abstract spaces 65J10 Numerical solutions to equations with linear operators
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