An efficient meshless radial point collocation method for nonlinear p-Laplacian equation

Boundary value problems

Thabet Abdeljawad¹  Mehdi Mesrizadeh²  Samaneh Soradi-Zeid³ 

[1] Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Medical Research, China Medical University, 40402, Taichung, Taiwan;Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan;Department of Mathematics, Kharazmi University, Karaj, Iran;Faculty of Industry and Mining (khash), University of Sistan and Baluchestan, Zahedan, Iran;

关键词: Collocation method;    Meshless method;    p;    Radial point interpolation technique;    Dirichlet and Neumann boundary conditions;   

DOI  :  10.1186/s13661-020-01457-7

来源: Springer

【 摘 要 】

This paper considered the spectral meshless radial point interpolation (SMRPI) method to unravel for the nonlinear p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions. Through this assessment, which includes meshless methods and collocation techniques based on radial point interpolation, we construct the shape functions, with the Kronecker delta function property, as basis functions in the framework of spectral collocation methods. Studies in this regard require one to evaluate the high-order derivatives without any kind of integration locally over the small quadrature domains. Finally, some examples are given to illustrate the low computing costs and high enough accuracy and efficiency of this method to solve a p-Laplacian equation and it would be of great help to fulfill the implementation related to the element-free Galerkin (EFG) method. Both the SMRPI and the EFG methods have been compared by similar numerical examples to show their application in strongly nonlinear problems.

【 授权许可】

CC BY