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Chin. Phys. B, 2021, Vol. 30(1): 010201    DOI: 10.1088/1674-1056/abaed7
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A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation

Yu Tan(谭渝) and Xiao-Lin Li(李小林)†
School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
Abstract  An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.
Keywords:  meshless      improved moving least square approximation      nonlinear improved Boussinesq equation      convergence and stability  
Revised:  26 July 2020      Published:  30 December 2020
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  03.65.Ge (Solutions of wave equations: bound states)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11971085), the Fund from the Chongqing Municipal Education Commission, China (Grant Nos. KJZD-M201800501 and CXQT19018), and the Chongqing Research Program of Basic Research and Frontier Technology, China (Grant No. cstc2018jcyjAX0266).
Corresponding Authors:  Corresponding author. E-mail: lxlmath@163.com   

Cite this article: 

Yu Tan(谭渝) and Xiao-Lin Li(李小林) A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation 2021 Chin. Phys. B 30 010201

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