Abstract
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.
Highlights
We are concerned for the numerical solution of the following nonlinear p-Laplacian equation:– div ∇u(x) p–2∇u(x) = f (x), x = (x1, x2) ∈, (1)with the Dirichlet and Neumann boundary conditions u(x) = g1(x), x = (x1, x2) ∈ 1, (2)n.∇u(x) = g2(x), x = (x1, x2) ∈ 2, (3)respectively
The shape functions corresponding to the nodal displacements of radial point interpolation method (RPIM), are the first n functions of the above vector and we show them by the vector T (x): (x) = φ1(x), φ2(x), . . . , φn(x)
5 Conclusion This paper is devoted to solving the p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions by the spectral meshless radial point interpolation (SMRPI) method
Summary
Introduction We are concerned for the numerical solution of the following nonlinear p-Laplacian equation: Because of the high efficiency of nonlinear term in the p-Laplacian equation, the EFG discretization results in highly nonlinear algebraic systems. The SMRPI method, comprised of meshless radial point interpolation and collocation techniques, has been assigned and applied to the 2-D and 3-D diffusion equations by Shivanian in [25,26,27,28].
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