Study on Vibration of Membranes with Taylor Polynomial Method and Error Analysis for Helmholtz Equation

Wang, Ke Yan; Wang, Qi Sheng

doi:10.4028/www.scientific.net/amr.763.234

Search citation statements

Order By: Relevance

Paper Sections

Select...

Relationship Between Partial Derivative Of Differential Equa...1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where I m and I n represent the unit matrices of m order and n order, respectively, and the D (2) and C (2) are barycentric interpolates of the second-order matrices at the node x 1 , x 2 , . .…”

Section: Relationship Between Partial Derivative Of Differential Equa...mentioning

confidence: 99%

See 1 more Smart Citation

A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation

Yang¹,

WentaoMa²,

Ge³

2021

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

In this paper, Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation. First of all, the interpolation basis function is applied to treat the spatial variables and their partial derivatives, and the collocation method for solving the second order di erential equations is established. Secondly, the di erential matrix is used to simplify the given di erential equations on a given test node. Finally, based on three kinds of test nodes, numerical experiments show that the present scheme can not only calculate the high wave numbers problems, but also calculate the variable wave numbers problems. In addition, the algorithm has the advantages of high calculation accuracy, good numerical stability and less time consuming.

show abstract

Section: Relationship Between Partial Derivative Of Differential Equa...mentioning

confidence: 99%

“…This equation can simulate a variety of physical phenomena, including vibration analysis, water wave propagation, electromagnetic scattering, acoustic scattering, and radar scattering, etc. [2][3][4][5][6]. There is a long history about the development of wave propagation [7].…”

Section: Introductionmentioning

confidence: 99%