Mohammad Tamsir
Department of Mathematics, Graphic Era (Deemed to be University), Dehradun-248002, Uttarakhand, India.

Neeraj Dhiman
Department of Mathematics, Graphic Era Hill University, Dehradun-248002, Uttarakhand, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.4-084

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Abstract

This work concerns for solving of coupled Burgers’ equations (CBEs) in 2D and 3D via DQM based on cubic trigonometric B-spline (CTB) shape functions. In the method, the shape functions are modified and used for the integration of space derivative. Consequently, the CBEs are transformed into the integral equations. These integral equations are solved by an “optimal strong stability-preserving Runge-Kutta method (SSP-RK54)”. Three examples are taken for analysis. The assessment of the present results are done with a number of already presented results in the literature. We initiated that the present method generates more precise results. Straightforward algorithm, little amount of computational cost and less error norms are the major achievements of the method. Therefore, the present method possibly will be very valuable optional method for the computation of nonlinear PDEs. Moreover, the analysis of method’s stability is also done.

Keywords- CBEs, DQM, CTB functions, SSP-RK54, Stability analysis.

Citation

Tamsir, M., & Dhiman, N. (2019). DQM Based on the Modified Form of CTB Shape Functions for Coupled Burgers’ Equation in 2D and 3D. International Journal of Mathematical, Engineering and Management Sciences, 4(4), 1051-1067. https://dx.doi.org/10.33889/IJMEMS.2019.4.4-084.