Accession Number : ADA119418

Title :   Wave Propagation and Stability for Finite Difference Schemes.

Descriptive Note : Doctoral thesis,


Personal Author(s) : Trefethen,Lloyd Nicholas

PDF Url : ADA119418

Report Date : May 1982

Pagination or Media Count : 106

Abstract : This dissertation investigates the behavior of finite difference models of linear hyperbolic partial differential equations. Whereas a hyperbolic equation is nondispersive and nondissipative, difference models are invariably dispersive, and often dissipative too. We set about analyzing them by means of existing techniques from the theory of dispersive wave propagation, making extensive use in particular of the concept of group velocity, the velocity at which energy propagates. The first three chapters present a general analysis of wave propagation in difference models. We describe systematically the effects of dispersion on numerical errors, for both smooth and parasitic waves. The reflection and transmission of waves at boundaries and interfaces are then studied at length. The key point for this is a distinction introduced here between leftgoing and rightgoing signals, which is based not on the characteristics of the original equation, but on the group velocities of the numerical model. The last three chapters examine stability for finite difference models of initial boundary value problems.

Descriptors :   *Linear differential equations, *Partial differential equations, *Finite difference theory, *Wave propagation, Stability, Dispersions, Mathematical models, Boundaries, Interfaces, Boundary value problems, Errors, Numerical analysis, Theses

Subject Categories : Numerical Mathematics
      Radiofrequency Wave Propagation

Distribution Statement : APPROVED FOR PUBLIC RELEASE