Numerical analysis of an ill-posed Cauchy problem for a convection--diffusion equation

Autor:	Lars Eldén, Zohreh Ranjbar
Rok vydání:	2007
Předmět:	Well-posed problem Cauchy problem Applied Mathematics Mathematical analysis General Engineering Singular integral Integral equation Volterra integral equation Computer Science Applications symbols.namesake Singular value Singular solution symbols Convection–diffusion equation Mathematics
Zdroj:	Inverse Problems in Science and Engineering. 15:191-211
ISSN:	1741-5985 1741-5977
DOI:	10.1080/17415970600557299
Popis:	The mathematical and numerical properties of an ill-posed Cauchy problem for a convection--diffusion equation are investigated in this study. The problem is reformulated as a Volterra integral equation of the first kind with a smooth kernel. The rate of decay of the singular values of the integral operator determines the degree of ill-posedness. The purpose of this article is to study how the convection term influences the degree of ill-posedness by computing numerically the singular values. It is also shown that the sign of the coefficient in the convection term determines the rate of decay of the singular values. Some numerical examples are also given to illustrate the theory.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c04c35293e2aff786938472fc4fdb58a https://doi.org/10.1080/17415970600557299 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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