Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Fourth order difference methods for the initial boundary-value problem for hyperbolic equations


Author: Joseph Oliger
Journal: Math. Comp. 28 (1974), 15-25
MSC: Primary 65N05
DOI: https://doi.org/10.1090/S0025-5718-1974-0359344-7
MathSciNet review: 0359344
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Centered difference approximations of fourth order in space and second order in time are applied to the mixed initial boundary-value problem for the hyperbolic equation $ {u_t} = - c{u_x}$. A method utilizing third order uncentered differences at the boundaries is shown to be stable and to retain an overall fourth order convergence estimate. Several computational examples illustrate the success of these methods for problems with one and two spacial dimensions. Further examples illustrate the effects of approximations of various orders of accuracy used at the boundaries.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N05

Retrieve articles in all journals with MSC: 65N05


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0359344-7
Article copyright: © Copyright 1974 American Mathematical Society