Abstract
A one-step new general mesh free scheme, which is based on radial basis functions, is presented for a viscous wave equation with variable coefficients. By constructing a simple extended radial basis function, it can be directly applied to wave propagation by using the strong form-based mesh free collocation method. There is no need to deal with the time-dependent variable particularly. Numerical results for a viscous wave equation with variable coefficients show that the proposed mesh free collocation method is simple with accurate solutions.
Highlights
The wave propagation exists in an interesting class of problems, such as the micro-scale heat transfer, seismic data acquisition and processing, etc
We aim to provide a truly mesh free method with one-step approximation, which is based on the radial basis functions (RBFs), for a viscous wave equation with variable coefficients
Most of them are based on the finite difference method, which lead to two-step methods
Summary
The wave propagation exists in an interesting class of problems, such as the micro-scale heat transfer, seismic data acquisition and processing, etc. Coupled with the FDM, the radial basis function (RBF) collocation methods are widely-used to many problems thanks to their mesh free features. Based on the integrated radial basis functions and a finite difference scheme, the regularized long-wave equations are investigated in [16, 17]. Oruc [18] examined numerical solutions of ZakharovRubenchik system by using radial basis function finite difference (RBF-FD) mesh less method and an explicit Runge-Kutta method. We aim to provide a truly mesh free method with one-step approximation, which is based on the RBFs, for a viscous wave equation with variable coefficients.
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