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

Ashyralyev, A.; Sobolevskii, P. E.

Abstr. Appl. Anal. 6, No. 2, 63-70 (2001).

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.

Reviewer: J.D.P.Donnelly (Oxford)

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

Keywords:

difference scheme; stability estimates; hyperbolic equation; Hilbert space