On families high-order accurate multioperator approximations of derivatives using two-point operators

Аннотация

A new family of multioperator approximations to derivatives of even and odd orders with inversion of two-point operators is considered. Existence and uniqueness theorems are stated for multioperators of formally arbitrary orders, and their spectral properties are examined. A scheme for a test hyperbolic equation with a multioperator approximation of 36th order is analyzed as an example. The accuracy and convergence of numerical solutions to the test problem are estimated.