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Jacobi Approximations in Certain Hilbert Spaces and Their Applications to Singular Differential Equations

✍ Scribed by Ben-yu Guo

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 241 KB
Volume: 243
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6677

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✦ Synopsis

Jacobi approximations in certain Hilbert spaces are investigated. Several weighted inverse inequalities and Poincare inequalities are obtained. Some approximation ŕesults are given. Singular differential equations are approximated by using Jacobi polynomials. This method keeps the spectral accuracy. Some linear problems and a nonlinear logistic equation are considered. The stabilities and the convergences of proposed schemes are proved strictly. The main idea and techniques used in this paper are also applicable to other singular problems in multiple-dimensional spaces.

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