Completion to involution and semidiscretisations
type: Item
instance of: scholarly article
title: Completion to involution and semidiscretisations
zbMATH Open document ID: 1004.65097
DOI: 10.1016/S0168-9274(01)00166-0
published in: Applied Numerical Mathematics
publication date: 2002-08-22T00:00:00Z
review text: The paper presents the formal concept of involution indices for differential algebraic equations. Starting with over-determined systems of partial differential equations with linear coefficients and no or periodic boundary conditions differential algebraic systems are obtained using semidiscretization. It is shown that the original partial differential equation is involutive if and only if the semi-discretized equations do not contain hidden constraints. Existence and uniqueness results for smooth solutions are proven by lifting a classical result for hyperbolic systems in Cauchy-Kovalevskaya form to overdetermined systems. Using finite difference and spectral methods for semi-discretization an equivalence between the integrability of the differential algebraic system and the property of the original system to be involutive is shown.
reviewed by: Kai Schneider
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 35L80
zbMATH DE Number: 1787747
zbMATH Keywords: c
zbMATH Keywords: differential algebraic equations
zbMATH Keywords: involution index
zbMATH Keywords: semidiscretization
zbMATH Keywords: hyperbolic systems
zbMATH Keywords: finite difference
zbMATH Keywords: spectral methods
author: Werner M. Seiler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787747