A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional ZK–BBM Equation

被引：1

作者：

Zabihi F. ^{[1
]}

Saffarian M. ^{[1
]}

机构：

[1] Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, P. O. Box 87317-53153, Kashan

来源：

International Journal of Applied and Computational Mathematics | 2017年 / 3卷 / 4期

关键词：

Collocation; Meshless method; Radial basis function (RBF); Thin plate splines (TPS); Two-dimensional ZK–BBM equation;

D O I：

10.1007/s40819-016-0287-z

中图分类号：

学科分类号：

摘要：

The main idea of this article is obtain the numerical solution of the two-dimensional ZK–BBM equation. We construct the solution by using different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. we use a predictor–corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme. © 2016, Springer India Pvt. Ltd.

引用

页码：4001 / 4013

页数：12

共 50 条

[21] Numerical solution to the unsteady two-dimensional Schrodinger equation using meshless local boundary integral equation method
Dehghan, Mehdi
Mirzaei, Davoud
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 76 (04) : 501 - 520
[22] Numerical comparisons of two meshless methods using radial basis functions
Li, JC
Hon, YC
Chen, CS
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2002, 26 (03) : 205 - 225
[23] Local Heaviside weighted MLPG meshless method for two-dimensional solids using compactly supported radial basis functions
Xiao, JR
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (1-2) : 117 - 138
[24] Numerical solution of RLW equation using radial basis functions
Dag, Idris
Dereli, Yilmaz
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (01) : 63 - 76
[25] Numerical solution of stochastic elliptic partial differential equations using the meshless method of radial basis functions
Dehghan, Mehdi
Shirzadi, Mohammad
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2015, 50 : 291 - 303
[26] A meshless method for the numerical solution of nonlinear weakly singular integral equations using radial basis functions
Assari, Pouria
Dehghan, Mehdi
EUROPEAN PHYSICAL JOURNAL PLUS, 2017, 132 (05):
[27] A meshless method for the numerical solution of nonlinear weakly singular integral equations using radial basis functions
Pouria Assari
Mehdi Dehghan
The European Physical Journal Plus, 132
[28] Meshless Method with Radial Basis Functions for Hamilton Canonical Equation
Li, Dinghe
Dou, Chen
Xu, Jianxin
ADVANCED ENGINEERING MATERIALS, PTS 1-3, 2011, 194-196 : 1407 - 1416
[29] The numerical solution of nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation via the meshless method of radial basis functions
Dehghan, Mehdi
Abbaszadeh, Mostafa
Mohebbi, Akbar
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 68 (03) : 212 - 237
[30] A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation
Shokri, Ali
Dehghan, Mehdi
COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (12) : 1990 - 2000

← 1 2 3 4 5 →