2016
DOI: 10.1137/15m1052391
|View full text |Cite
|
Sign up to set email alerts
|

Müntz--Galerkin Methods and Applications to Mixed Dirichlet--Neumann Boundary Value Problems

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4

Citation Types

0
17
0

Year Published

2017
2017
2021
2021

Publication Types

Select...
8

Relationship

0
8

Authors

Journals

citations
Cited by 43 publications
(17 citation statements)
references
References 16 publications
0
17
0
Order By: Relevance
“…Also, in Bahmanpour et al (2019), Müntz wavelet combination with a matrix method was introduced to solve Fredholm integral equations of the first kind. Shen and Wang (2016) develop a Müntz-Galerkin method to deal with the singular behaviors of the mixed Dirichlet-Neumann boundary value problems and obtained optimal error estimates.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations
“…Also, in Bahmanpour et al (2019), Müntz wavelet combination with a matrix method was introduced to solve Fredholm integral equations of the first kind. Shen and Wang (2016) develop a Müntz-Galerkin method to deal with the singular behaviors of the mixed Dirichlet-Neumann boundary value problems and obtained optimal error estimates.…”
Section: Introductionmentioning
confidence: 99%
“…Direct evaluation of M-L polynomials and their fractional derivatives are numerically poorly conditioned (Esmaeili et al 2011;Shen and Wang 2016). Although some numerical methods based on M-L polynomials have been proposed for fractional problems, there are not many stable methods for evaluating the fractional derivatives of M-L polynomials (Bahmanpour et al 2018;Ejlali and Hosseini 2016;Hosseinpour et al 2019;Mokhtary et al 2016).…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…With a priori knowledge of the singularity of the underlying solution, such a tool can provide very accurate approximation to a large class of singular problems with suitable choices of { k } (see, e.g., [2,35,36]). Recently, Shen and Wang [43] associated the Müntz polynomials with Jacobi polynomials and developed efficient and accurate Müntz-Galerkin methods for some singular problems with typical singularities of the type: k = k with ∈ (0, 1). Hou and Xu [17] further studied the so-called factional Jacobi polynomials: J , , n (x) = J , n (2x − 1) for x ∈ (0, 1), , > −1 and > 0, with applications to the integral-differential and fractional differential equations.…”
Section: Introductionmentioning
confidence: 99%
“…In analogy to those in [17] designed for d dimensional ball, a class of Sobolev orthogonal Müntz-Hermite functions on the whole space, L αn k (r 2 )e − r 2 2 r αn+1− d 2 Y n (ξ), can be presented to incorporate the singularity r αn+1−d/2 . Readers refer to [1,26] for more about Müntz polynomials and their applications in spectral methods in one dimension. In the sequel, a novel spectral method using these genuine Hermite functions is proposed to achieve an exponential rate of convergence together with a highly efficient implementation.…”
mentioning
confidence: 99%