Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces.

*(English)*Zbl 1002.65101The problem of stability of difference schemes for second-order evolution equations is considered. The difference schemes are treated as abstract Cauchy problems for difference equations with operator coefficients in a Banach or Hilbert space. The regularization principle is employed to construct stable difference schemes. It starts from any simple scheme and derives absolutely stable schemes by perturbing the operator coefficients.

The aim of this paper is to obtain stability results for regularized three-level difference schemes with unbounded operator coefficients in a Banach space. For example this class of schemes arises when approximating second-order evolution differential equations.

The aim of this paper is to obtain stability results for regularized three-level difference schemes with unbounded operator coefficients in a Banach space. For example this class of schemes arises when approximating second-order evolution differential equations.

Reviewer: L.Hącia (Poznań)

##### 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 |

65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |

65J10 | Numerical solutions to equations with linear operators |

34G10 | Linear differential equations in abstract spaces |

35K90 | Abstract parabolic equations |