Kernel optimum nearly-analytical discretization (KOND) algorithm applied to parabolic and hyperbolic equations
type: Item
instance of: scholarly article
title: Kernel optimum nearly-analytical discretization (KOND) algorithm applied to parabolic and hyperbolic equations
zbMATH Open document ID: 0796.65101
DOI: 10.1016/0898-1221(94)90047-7
author: V. Pereyra
publication date: 1994-06-23T00:00:00Z
review text: Two applications of the kernel optimum nearly-analytical discretization (KOND) algorithm to parabolic and hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy. It is demonstrated numerically that the two-dimensional KOND-P scheme for the parabolic type yields much less numerical error by over 2- 3 orders, measured quantitatively by the root mean square deviation from analytic solutions, and reduces the CPU time to about 1/5 for a common numerical accuracy, compared with the conventional explicit scheme of reference. It is also demonstrated numerically that the KOND-H scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both the linear and the nonlinear wave propagation compared with other conventional schemes. Origins of numerical errors in data processing in general numerical schemes are discussed.
reviewed by: Michael Sever
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 571514
zbMATH Keywords: kernel optimum nearly-analytical discretization algorithm
zbMATH Keywords: stability
zbMATH Keywords: nonlinear wave propagations
MaRDI profile type: Publication
full work available at URL: 0898-1221(94)90047-7
OpenAlex ID: W2073794775
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published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 571514