Truncation and accumulated errors in wave propagation

Document Type

Article

Publication Date

1-1-1988

Abstract

The approximation of the truncation and accumulated errors in the numerical solution of a linear initial-valued partial differential equation problem can be established by using a semidiscretized scheme. This error approximation is observed as a lower bound to the errors of a finite difference scheme. By introducing a modified von Neumann solution, this error approximation is applicable to problems with variable coefficients. To seek an in-depth understanding of this newly established error approximation, numerical experiments were performed to solve the hyperbolic equation ∂U ∂t = -C1(x)C2(t) ∂U ∂x, with both continuous and discontinuous initial conditions. We studied three cases: (1)C1(x)=C0 and C2(t)=1; (2) C1(x)=C0 and C2(t=t; and (3) C1(x)=1+( solx a)2 and C2(t)=C0. Our results show that the errors are problem dependent and are functions of the propagating wave speed. This suggests a need to derive problem-oriented schemes rather than the equation-oriented schemes as is commonly done. Furthermore, in a wave-propagation problem, measurement of the error by the maximum norm is not particularly informative when the wave speed is incorrect. © 1988.

Identifier

45449121270 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/0021-9991(88)90021-6

e-ISSN

10902716

ISSN

00219991

First Page

353

Last Page

372

Issue

2

Volume

79

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