An Efficient Local Formulation for Time-Dependent PDEs

被引：27

作者：

Ahmad, Imtiaz ^{[1
]}

Ahsan, Muhammad ^{[1
,2
]}

Din, Zaheer-ud ^{[2
,3
]}

Ahmad, Masood ^{[2
]}

Kumam, Poom ^{[4
,5
]}

机构：

[1] Univ Swabi, Dept Math, Swabi 23430, Pakistan

[2] Univ Engn & Technol, Dept Basic Sci, Peshawar 25000, Pakistan

[3] CECOS Univ IT & Emerging Sci, Dept Basic Sci, Peshawar 25000, Pakistan

[4] KMUTT, Fac Sci, Dept Math, KMUTT Fixed Point Res Lab, Room SCL 802 Fixed Point Lab,Sci Lab Bldg, Bangkok 10140, Thailand

[5] KMUTT, Fac Sci, Theoret & Computat Sci Ctr TaCS, KMUTT Fixed Point Theory & Applicat Res Grp, Sci Lab Bldg,126 Pracha Uthit Rd, Bangkok 10140, Thailand

来源：

MATHEMATICS | 2019年 / 7卷 / 03期

关键词：

local meshless method; RBFs; irregular domains; Kortewege-de Vries types equations; reaction-diffusion Brusselator system; FITZHUGH-NAGUMO EQUATION; VARIATIONAL ITERATION METHOD; DE-VRIES EQUATION; NUMERICAL-SOLUTIONS; BURGERS-HUXLEY; DECOMPOSITION METHOD; SOLITON-SOLUTIONS; FISHER; COLLOCATION; EXPLICIT;

D O I：

10.3390/math7030216

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.

引用

页数：18

共 52 条

[1] Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method [J].