A representation and approximation of the solutions of hyperbolic differential equations
type: Item
instance of: scholarly article
title: A representation and approximation of the solutions of hyperbolic differential equations
zbMATH Open document ID: 0641.65085
DOI: 10.1016/0021-9991(87)90138-0
author: S. Raj Vatsya
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: A system of quasilinear hyperbolic partial differential equations is discussed for a qualitative study of weak solutions and for developing a suitable numerical scheme. The Stieltjes transform and its properties are used to reduce the system of equations to a fixed point equation which is put in a computationally feasible form after comparing it with the method of characteristics. A discontinuous or piecewise continuous profile may be assumed for the initial approximation. The equations of fluid flow in an ideal shock tube are discussed using this method and the following improvements are noted: Spurious oscillations are absent, the resolution and accuracy of the location of the discontinuities are excellent; the constant state is adequately realized; and the diffusion is minimal.
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65M25
Mathematics Subject Classification ID: 35A22
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 4045071
zbMATH Keywords: comparison of methods
zbMATH Keywords: quasilinear
zbMATH Keywords: weak solutions
zbMATH Keywords: Stieltjes transform
zbMATH Keywords: fixed point equation
zbMATH Keywords: method of characteristics
zbMATH Keywords: fluid flow in an ideal shock tube
zbMATH Keywords: Spurious oscillations
zbMATH Keywords: location of the discontinuities
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90138-0
OpenAlex ID: W2098113185
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description: scientific article; zbMATH DE number 4045071