The radial basis function finite collocation approach for capturing sharp fronts in time dependent advection problems

2015 ◽  
Vol 298 ◽  
pp. 423-445 ◽  
Author(s):  
D. Stevens ◽  
H. Power
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Time Dependent ◽  
Radial Basis ◽  
Sharp Fronts ◽  
Collocation Approach

scholarly journals A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fuzhang Wang ◽  
Enran Hou
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Meshless Method ◽  
Space Variable ◽  
Second Order ◽  
Time Variable ◽  
Time Dependent ◽  
Two Dimensional ◽  
Radial Basis ◽  
Telegraph Equations

In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods.

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