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Title: Log orthogonal functions: approximation properties and applications
Abstract We present two new classes of orthogonal functions, log orthogonal functions and generalized log orthogonal functions, which are constructed by applying a $\log $ mapping to Laguerre polynomials. We develop basic approximation theory for these new orthogonal functions, and apply them to solve several typical fractional differential equations whose solutions exhibit weak singularities. Our error analysis and numerical results show that our methods based on the new orthogonal functions are particularly suitable for functions that have weak singularities at one endpoint and can lead to exponential convergence rate, as opposed to low algebraic rates if usual orthogonal polynomials are used.  more » « less
Award ID(s):
2012585
NSF-PAR ID:
10329288
Author(s) / Creator(s):
;
Date Published:
Journal Name:
IMA Journal of Numerical Analysis
Volume:
42
Issue:
1
ISSN:
0272-4979
Page Range / eLocation ID:
712 to 743
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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