Unified and extended trigonometric B-spline DQM for the numerical treatment of three-dimensional wave equations

Abstract

In this work, we propose a new differential quadrature method (DQM) based on the Unified and Extended Trigonometric B-spline (UETB-spline) functions for the numerical approximation of 3D wave equations. The UETB -spline functions are modified and then utilized in DQM to compute the weighting coefficients of spatial derivatives. After inverting the obtained coefficients, we acquire systems of ODEs that are solved by the SSP-RK5,4 scheme. Some numerical examples are considered to examine the accuracy and proficiency of the proposed approach. The obtained solutions give excellent agreement with analytical solutions. Moreover, the analysis for the rate of convergence (ROC) is performed. Computational complexity exhibits that the approach is not complex in the view of the computational cost. All calculations have been done using Dev-C++ 6.3 version and graphs have been plotted using MATLAB 2015b software.

Keywords

• 65Mxx
• 65Nxx