Result: A Rational Approximation and Its Applications to Differential Equations on the Half Line: A rational approximation and its applications to differential equations on the half line
Title:
A Rational Approximation and Its Applications to Differential Equations on the Half Line: A rational approximation and its applications to differential equations on the half line
Authors:
Source:
Journal of Scientific Computing. 15:117-147
Publisher Information:
Springer Science and Business Media LLC, 2000.
Publication Year:
2000
Subject Terms:
Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Heat equation, pseudospectral method, rational interpolation, differential equations on the half line, orthogonal rational functions, spectral method, numerical results, 01 natural sciences, Approximation by rational functions, Numerical interpolation, Legendre polynomials, Linear boundary value problems for ordinary differential equations, 0101 mathematics, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1573-7691
0885-7474
0885-7474
DOI:
10.1023/a:1007698525506
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....2e90abaf6e6eb1adf200d11db1d6c74d
Database:
OpenAIRE
Further Information
The system of orthogonal rational functions induced by the Legendre polynomials and its basic properties are introduced. Various orthogonal projections are studied and established some results on rational approximation are established. Two kinds of rational interpolation are considered. A rational spectral method and a rational pseudospectral method for two model problems are analyzed. Finally, some numerical implementations and numerical results are presented which agree well with the theoretical analysis and which demonstrate the effectiveness of the considered approach.