High-order schemes for conservative or dissipative systems
The author presents a new approach to the design of finite difference methods. The paper focuses on the need to develop discrete schemes for solving conservative or dissipative initial value problems such as Hamiltonian systems without damping. The author begins by presenting (as Scheme 1) a first or second order finite difference scheme. In Scheme 2 he provides a general \(p\)-th order scheme which requires starting values in addition to the initial values. The order of the scheme is proved as its property to preserve the conservative or dissipative nature of the underlying problem. The paper concludes with some numerical examples and the author draws attention to the attractive feature that computational costs do not rise with the order of acuracy.
scientific article; zbMATH DE number 1912275