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New Log Basis Functions with a Scaling Factor and Their Applications

New Log Basis Functions with a Scaling Factor and Their Applications

Year:    2024

Author:    Dong-Qin Gu, Dongya Tao, Chao Zhang

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2024-0038

Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 4 : pp. 1018–1040

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

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

Author Details

Dong-Qin Gu

Dongya Tao

Chao Zhang