Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines

被引：7

作者：

Hussain, Arshad ^{[1
]}

Uddin, Marjan ^{[1
,2
]}

Haq, Sirajul ^{[1
,3
]}

Jan, Hameed Ullah ^{[1
,2
]}

机构：

[1] Karakoram Int Univ, Dept Math, Hunza Campus, Gilgit Baltistan, Pakistan

[2] UET, Dept Basic Sci & Islamiat, Pehsawar, Khyber Pakhtunk, Pakistan

[3] GIK Inst Engn Sci & Technol, Fac Engn Sci, Topi, Khyber Pakhtunk, Pakistan

来源：

JOURNAL OF MATHEMATICS | 2021年 / 2021卷

关键词：

DATA APPROXIMATION SCHEME; ORDER DIFFERENCE-METHODS; SCATTERED DATA; MULTIQUADRICS; STABILITY; ACCURACY;

D O I：

10.1155/2021/8862139

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose a numerical solution to the heat equation in polar cylindrical coordinates by using the meshless method of lines approach. The space variables are discretized by multiquadric radial basis function, and time integration is performed by using the Runge-Kutta method of order 4. In radial basis functions (RBFs), much of the research are devoted to the partial differential equations in rectangular coordinates. This work is an attempt to explore the versatility of RBFs in nonrectangular coordinates as well. The results show that application of RBFs is equally good in polar cylindrical coordinates. Comparison with other cited works confirms that the present approach is accurate as well as easy to implement to problems in higher dimensions.

引用

页数：11

共 34 条

[11] Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory [J].

Gu, Yan ;

Fan, Chia-Ming ;

Fu, Zhuojia .

ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 13 (06) :1520-1534

[12] Method of lines solutions of the extended Boussinesq equations [J].

Hamdi, S ;

Enright, WH ;

Ouellet, Y ;

Schiesser, WE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 183 (02) :327-342

[13] On the numerical solution of nonlinear Burgers'-type equations using meshless method of lines [J].

Haq, Sirajul ;

Hussain, Arshad ;

Uddin, Marjan .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (11) :6280-6290

[14]

Hu S.S., 1981, ADV COMPUTER METHODS, P305

[15] Numerical solution of Klein-Gordon and sine-Gordon equations by meshless method of lines [J].

Hussain, Arshad ;

Haq, Sirajul ;

Uddin, Marjan .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2013, 37 (11) :1351-1366

[16] HIGH-ORDER DIFFERENCE-METHODS FOR HEAT-EQUATION IN POLAR CYLINDRICAL COORDINATES [J].

IYENGAR, SRK ;

MANOHAR, R .

JOURNAL OF COMPUTATIONAL PHYSICS, 1988, 77 (02) :425-438

[17]

IYENGAR SRK, 1978, J I MATH APPL, V22, P321

[18] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .1. [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :127-145

[19] MULTIQUADRICS - A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS .2. SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS [J].

KANSA, EJ .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1990, 19 (8-9) :147-161

[20] Local artificial boundary conditions for Schrodinger and heat equations by using high-order azimuth derivatives on circular artificial boundary [J].

Li, Hongwei ;

Wu, Xiaonan ;

Zhang, Jiwei .

COMPUTER PHYSICS COMMUNICATIONS, 2014, 185 (06) :1606-1615

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