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Volume 17, Issue 4
New Log Basis Functions with a Scaling Factor and Their Applications

Dong-Qin Gu, Dongya Tao & Chao Zhang

DOI: 10.4208/nmtma.OA-2024-0038

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 1018-1040.

Published online: 2024-12

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  • Abstract

In the paper, we introduce two new classes of orthogonal functions, new log orthogonal functions (NLOFs) and generalized new log orthogonal functions (GNLOFs), which are based on generalized Laguerre polynomials. We construct basis approximations analysis for the new orthogonal functions and apply them to solve several typical differential equations. Our errors analysis and numerical results show that our methods based on the new orthogonal functions are particularly suitable for functions which have weak singularities at one endpoint, and can obtain exponential convergence rate, as opposed to low algebraic rates if usual orthogonal polynomials are used.

  • Keywords

New log orthogonal function, generalized Laguerre functions, singularity, fractional differential equations.

  • AMS Subject Headings

65M70, 65N35, 42A05, 65N35, 41A25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{NMTMA-17-1018, author = {Gu , Dong-QinTao , Dongya and Zhang , Chao}, title = {New Log Basis Functions with a Scaling Factor and Their Applications}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {4}, pages = {1018--1040}, abstract = {

In the paper, we introduce two new classes of orthogonal functions, new log orthogonal functions (NLOFs) and generalized new log orthogonal functions (GNLOFs), which are based on generalized Laguerre polynomials. We construct basis approximations analysis for the new orthogonal functions and apply them to solve several typical differential equations. Our errors analysis and numerical results show that our methods based on the new orthogonal functions are particularly suitable for functions which have weak singularities at one endpoint, and can obtain exponential convergence rate, as opposed to low algebraic rates if usual orthogonal polynomials are used.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0038}, url = {http://global-sci.org/intro/article_detail/nmtma/23650.html} }
TY - JOUR T1 - New Log Basis Functions with a Scaling Factor and Their Applications AU - Gu , Dong-Qin AU - Tao , Dongya AU - Zhang , Chao JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1018 EP - 1040 PY - 2024 DA - 2024/12 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2024-0038 UR - https://global-sci.org/intro/article_detail/nmtma/23650.html KW - New log orthogonal function, generalized Laguerre functions, singularity, fractional differential equations. AB -

In the paper, we introduce two new classes of orthogonal functions, new log orthogonal functions (NLOFs) and generalized new log orthogonal functions (GNLOFs), which are based on generalized Laguerre polynomials. We construct basis approximations analysis for the new orthogonal functions and apply them to solve several typical differential equations. Our errors analysis and numerical results show that our methods based on the new orthogonal functions are particularly suitable for functions which have weak singularities at one endpoint, and can obtain exponential convergence rate, as opposed to low algebraic rates if usual orthogonal polynomials are used.

Gu , Dong-QinTao , Dongya and Zhang , Chao. (2024). New Log Basis Functions with a Scaling Factor and Their Applications. Numerical Mathematics: Theory, Methods and Applications. 17 (4). 1018-1040. doi:10.4208/nmtma.OA-2024-0038
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