Compactly supported radial basis functions for solving certain high order partial differential equations in 3D

2015 ◽  
Vol 55 ◽  
pp. 2-9 ◽  
Author(s):  
Wen Li ◽  
Ming Li ◽  
C.S. Chen ◽  
Xiaofeng Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Radial Basis Functions ◽  
High Order ◽  
Basis Functions ◽  
Partial Differential ◽  
Compactly Supported ◽  
Radial Basis

scholarly journals A Multiscale RBF Collocation Method for the Numerical Solution of Partial Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 964 ◽  
Author(s):  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Radial Basis Functions ◽  
Computational Cost ◽  
Basis Functions ◽  
Partial Differential ◽  
Compactly Supported ◽  
Linear Partial Differential Equations ◽  
Numerical Experimentation ◽  
Radial Basis

In this paper, we derive and discuss the hierarchical radial basis functions method for the approximation to Sobolev functions and the collocation to well-posed linear partial differential equations. Similar to multilevel splitting of finite element spaces, the hierarchical radial basis functions are constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii. Compared with the compactly supported radial basis functions approximation and stationary multilevel approximation, the new method can not only solve the present problem on a single level with higher accuracy and lower computational cost, but also produce a highly sparse discrete algebraic system. These observations are obtained by taking the direct approach of numerical experimentation.

The Coupling of RBF and FDM for Solving Higher Order Fractional Partial Differential Equations

2014 ◽  
Vol 598 ◽  
pp. 409-413 ◽  
Author(s):  
Zakieh Avazzadeh ◽  
Wen Chen ◽  
Vahid Reza Hosseini
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Discrete Solution ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Time Direction ◽  
Radial Basis

In this work, we describe the radial basis functions for solving the time fractional partial differential equations defined by Caputo sense. These problems can be discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. Numerical results accuracy the efficiency of the presented method.

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