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
收藏
页码：230 / 236
页数：7
相关论文
共 50 条
[21]   Numerical Solution of Direct and Inverse Problems for Time-Dependent Volterra Integro-Differential Equation Using Finite Integration Method with Shifted Chebyshev Polynomials [J].
Boonklurb, Ratinan ;
Duangpan, Ampol ;
Gugaew, Phansphitcha .
SYMMETRY-BASEL, 2020, 12 (04)
[22]   Electromagnetic Field Computation Using Space-Time Grid and Finite Integration Method [J].
Matsuo, Tetsuji .
IEEE TRANSACTIONS ON MAGNETICS, 2010, 46 (08) :3241-3244
[23]   Space-Time Grids for Electromagnetic Field Computation Using Finite Integration Method [J].
Shimizu, S. ;
Mifune, T. ;
Matsuo, T. .
2011 IEEE INTERNATIONAL SYMPOSIUM ON ANTENNAS AND PROPAGATION (APSURSI), 2011, :2346-2349
[24]   Application of the Quadrature-Difference Method for Solving Fredholm Integro-Differential Equations [J].
Jalius, C. ;
Majid, Z. A. .
2015 INTERNATIONAL CONFERENCE ON RESEARCH AND EDUCATION IN MATHEMATICS (ICREM7), 2015, :66-70
[25]   Numerical simulation on FSI characteristics of fluid-conveying straight pipe by finite integration method [J].
Zhang T. ;
Guo X.-M. ;
Tan Z.-X. ;
Hu Y. .
Zhendong Gongcheng Xuebao/Journal of Vibration Engineering, 2019, 32 (01) :160-167
[26]   A PRIORI ERROR ESTIMATES FOR FINITE VOLUME ELEMENT APPROXIMATIONS TO SECOND ORDER LINEAR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATIONS [J].
Karaa, Samir ;
Pani, Amiya K. .
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2015, 12 (03) :401-429
[27]   A New One-Step Method Inverse Polynomial Method for Solving Stiff and Non-Stiff Delay Differential Equations [J].
Shaalini, J. Vinci ;
Fadugba, S. E. .
JOURNAL OF ALGEBRAIC STATISTICS, 2022, 13 (02) :1072-1081
[28]   Adaptive fractional physical information neural network based on PQI scheme for solving time-fractional partial differential equations [J].
Yang, Ziqing ;
Niu, Ruiping ;
Chen, Miaomiao ;
Jia, Hongen ;
Li, Shengli .
ELECTRONIC RESEARCH ARCHIVE, 2024, 32 (04) :2699-2727
[29]   A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations [J].
Zuniga-Aguilar, C. J. ;
Gomez-Aguilar, J. F. ;
Escobar-Jimenez, R. F. ;
Romero-Ugalde, H. M. .
CHAOS SOLITONS & FRACTALS, 2019, 126 :266-282
[30]   Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients [J].
Biazar, Jafar ;
Asadi, Mohammad Ali .
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2019, 7 (01) :1-15
12345