Improved finite integration method for partial differential equations

被引：18

作者：

Li, M. ^{[1
]}

Tian, Z. L. ^{[1
]}

Hon, Y. C. ^{[1
,2
]}

Chen, C. S. ^{[1
,3
]}

Wen, P. H. ^{[4
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Taiyuan, Peoples R China

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[3] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA

[4] Univ London, Sch Engn & Mat Sci, London E1 4NS, England

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2016年 / 64卷

基金：

中国国家自然科学基金;

关键词：

Finite integration method; Numerical quadrature; Simpson's rule; Cotes integral formula; Lagrange interpolation;

D O I：

10.1016/j.enganabound.2015.12.012

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Based on the recently developed finite integration method (FIM) for solving one-dimensional partial differential equations by using the trapezoidal rule for numerical quadrature, we improve in this paper the FIM with an alternative extended Simpson's rule in which the Cotes and Lagrange formulas are used to determine the first order integral matrix. The improved one-dimensional FIM is then further extended to solve two-dimensional problems. Numerical comparison with the finite difference method and the FIM (Trapezoidal rule) are performed by several one- and two-dimensional real application including the Poisson type differential equations and plate bending problems. It has been shown that the newly revised FIM has made significant improvement in terms of accuracy compare without much sacrifice on the stability and efficiency. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：230 / 236

页数：7

共 50 条

[31] Numerical solution of functional differential, integral and integro-differential equations [J].

Rashed, MT .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 156 (02) :485-492

[32] Generating differential equations satisfied by products of functions [J].

Chung, KC .

APPLIED MATHEMATICS LETTERS, 2001, 14 (07) :885-889

[33] Adaptive least squares finite integration method for higher-dimensional singular perturbation problems with multiple boundary layers [J].

Yun, D. F. ;

Wen, Z. H. ;

Hon, Y. C. .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 271 :232-250

[34] Efficient integration of crack singularities in the extended finite element method: Duffy-distance transformation and conformal preconditioning strategy [J].

Lv, Jia-He ;

Jiao, Yu-Yong ;

Wriggers, Peter ;

Rabczuk, Timon ;

Feng, Xia-Ting ;

Tan, Fei .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 340 :559-576

[35] Determination of Unknown Time-Dependent Heat Source in Inverse Problems under Nonlocal Boundary Conditions by Finite Integration Method [J].

Hazanee, Areena ;

Makaje, Nifatamah .

KYUNGPOOK MATHEMATICAL JOURNAL, 2024, 64 (02) :353-369

[36] Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations [J].

Rashed, MT .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 151 (03) :869-878

[37] Efficient quadrature rules for finite element discretizations of nonlocal equations [J].

Aulisa, Eugenio ;

Capodaglio, Giacomo ;

Chierici, Andrea ;

D'Elia, Marta .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2022, 38 (06) :1767-1793

[38] Finite element methods with numerical quadrature for parabolic integrodifferential equations [J].

Pani, AK ;

Peterson, TE .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1996, 33 (03) :1084-1105

[39] Improved numerical integration for analytical photon distribution calculation in SPECT [J].

Humphries, T. ;

Celler, A. ;

Trummer, M. R. .

2007 IEEE NUCLEAR SCIENCE SYMPOSIUM CONFERENCE RECORD, VOLS 1-11, 2007, :3548-+

[40] Efficient integration method for fictitious domain approaches [J].

Duczek, Sascha ;

Gabbert, Ulrich .

COMPUTATIONAL MECHANICS, 2015, 56 (04) :725-738

← 1 2 3 4 5 →