A general method for obtaining unconventional and nonstandard difference schemes
In recent years unconventional and nonstandard difference schemes were introduced for individual differential equations. Some of these are exact schemes, others give dynamically correct approximations for wide parameter ranges and arbitrary initial values even in the case of blow-up, or they are symplectic on a non-canonical Hamiltonian system. In this paper it is shown that a number of such unconventional and nonstandard schemes for ordinary and partial differential equations are generated by a general method: the linearized trapezoidal rule. Moreover, the method is fairly standard: practitioners in computational plasma physics and fluid dynamics have been using it for years and it belongs to the family of Rosenbrock methods.
Bibliographic Reference: Article: Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 3 (1997) pp. 453-467
Record Number: 199810305 / Last updated on: 1998-03-09
Original language: en
Available languages: en