A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation

Shokri A.; Dehghan M.

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A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation

机译：改进的Boussinesq方程数值解的径向基函数和预测校正方案的非非结无网格方法

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A numerical simulation of the improved Boussinesq (IBq) equation is obtained using collocation and approximating the solution by radial basis functions (RBFs) based on the third-order time discretization. To avoid solving the nonlinear system, a predictor-corrector scheme is proposed and the Not-a-Knot method is used to improve the accuracy in the boundary. The method is tested on two problems taken from the literature: propagation of a solitary wave and interaction of two solitary waves. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the new scheme presented in this paper.

机译：使用搭配并基于三阶时间离散化的径向基函数（RBF）逼近解，获得了改进的Boussinesq（IBq）方程的数值模拟。为了避免求解非线性系统，提出了一种预测校正器方案，并采用Not-a-Knot方法提高了边界精度。在从文献中得出的两个问题上测试了该方法：孤波的传播和两个孤波的相互作用。将数值实验的结果与解析解以及其他最近发表的方法的结果进行比较，以确认本文提出的新方案的准确性和效率。

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《Computer physics communications》 |2010年第12期|共11页
作者
Shokri A.; Dehghan M.;
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正文语种 eng
中图分类计算机的应用;
关键词
Boussinesq equation (Bq); Collocation; Improved Boussinesq equation (IBq); Meshless method; Multiquadrics (MQ); Not-a-Knot method; Predictor-corrector scheme; Radial basis functions (RBFs);

机译：Boussinesq方程（Bq）;定位;改进的Boussinesq方程（IBq）;无网格方法;多二次方（MQ）;非a-Knot方法;预测校正方案;径向基函数（RBF）;

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1. A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation [J] . Shokri A., Dehghan M. Computer physics communications . 2010,第12期

机译：改进的Boussinesq方程数值解的径向基函数和预测校正方案的非非结无网格方法
2. The numerical solution of nonlinear generalized Benjamin-Bona-Mahony-Burgers and regularized long-wave equations via the meshless method of integrated radial basis functions [J] . Ali Ebrahimijahan, Mehdi Dehghan Engineering with Computers . 2021,第1期

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3. On the numerical solution of fractional stochastic integro-differential equations via meshless discrete collocation method based on radial basis functions [J] . Mirzaee Farshid, Samadyar Nasrin Engineering analysis with boundary elements . 2019,第MARa期

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4. A NUMERICAL METHOD FOR THE GENERALIZED BOUSSINESQ EQUATION USING COLLOCATION AND RADIAL BASIS FUNCTIONS [C] . Abdur Rashid Applied simulation and modelling ; Artificial intelligence and soft computing . 2012

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5. Adaptive radial basis function methods for the numerical solution of partial differential equations, with application to the simulation of the human tear film. [D] . Heryudono, Alfa R. H. 2008

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6. Study of analytical method to seek for exact solutions of variant Boussinesq equations [O] . Kamruzzaman Khan, M Ali Akbar -1

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7. Numerical Study of Astrophysics Equations by Meshless Collocation Method Based on Compactly Supported Radial Basis Function [O] . Parand, Kourosh, Hemami, Mohammad 2016

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8. A Meshless Method Using Radial Basis Functions for Beam Bending Problems [R] . Raju, I. S., Phillips, D. R., Krishnamurthy, T. 2004

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A Not-a-Knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation

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