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Soradi-Zeid, Samaneh; Mesrizadeh, Mehdi; Abdeljawad, Thabet

An efficient meshless radial point collocation method for nonlinear \(p\)-Laplacian equation. (English) Zbl 1493.65248

Bound. Value Probl. 2020, Paper No. 161, 13 p. (2020).
Summary: 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.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65D12 Numerical radial basis function approximation
35J62 Quasilinear elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian

Keywords:

collocation method; meshless method; \(p\)-Laplacian equation; radial point interpolation technique; Dirichlet and Neumann boundary conditions
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