Since the governing equation of the problem considered is complex, and the corresponding physical domain or the boundary conditions are tangle some, the analytical solutions are almost inaccessible for most practical engineering problems. Related works can be found in and references therein. Such problems have been widely investigated because of their realistic physical background. Acoustic wave modeling is an essential part of the technique of acoustic imaging. The wave propagation exists in an interesting class of problems, such as the micro-scale heat transfer, seismic data acquisition and processing, etc. Numerical results for a viscous wave equation with variable coefficients show that the proposed mesh free collocation method is simple with accurate solutions.

There is no need to deal with the time-dependent variable particularly.

$fasshauer meshfree methods$

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.

5Section of Mathematics, International Telematic University Uninettuno, Roma, ItalyĪ one-step new general mesh free scheme, which is based on radial basis functions, is presented for a viscous wave equation with variable coefficients.

4Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.

3Department of Mathematics, University of Swabi, Swabi, Pakistan.

2School of Computer Science and Technology, Huaibei Normal University, Huaibei, China.

1College of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, China.

Fuzhang Wang 1,2, Juan Zhang 2*, Imtiaz Ahmad 3, Aamir Farooq 4 and Hijaz Ahmad 5

Fasshauer meshfree methods