Numerical solution of a non-classical two-phase Stefan problem via radial basis function (RBF) collocation methods

2016 ◽  
Vol 72 ◽  
pp. 111-127 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mahboubeh Najafi
Keyword(s):  
Radial Basis Function ◽  
Numerical Solution ◽  
Stefan Problem ◽  
Basis Function ◽  
Collocation Methods ◽  
Two Phase ◽  
Radial Basis

scholarly journals On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Nonlinear Partial Differential Equation ◽  
Multiscale Methods ◽  
Collocation Methods ◽  
Numerical Experimentation ◽  
Radial Basis ◽  
Monge Ampere ◽  
Radial Basis Function Method

This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampère equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods. The first method is the cascadic meshfree method, which was proposed by Liu and He (2013). The second method is the stationary multilevel method, which was proposed by Floater and Iske (1996), and is used to solve the fully nonlinear partial differential equation in the paper for the first time. The third is the hierarchical radial basis function method, which is constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii. Compared with the first two methods, the hierarchical radial basis function method can not only solve the present problem on a single level with higher accuracy and lower computational cost but also produce highly sparse nonlinear discrete system. These observations are obtained by taking the direct approach of numerical experimentation.

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