DQM Based on the Modified Form of CTB Shape Functions for Coupled Burgers’ Equation in 2D and 3D

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 inte...

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Bibliographic Details
Published in:International journal of mathematical, engineering and management sciences engineering and management sciences, 2019-08, Vol.4 (4), p.1051-1067
Main Authors: Tamsir, Mohammad, Dhiman, Neeraj
Format: Article
Language:English
Subjects:
CBEs
CTB functions
DQM
Integral equations
SSP-RK54
Stability analysis
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Summary: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.
ISSN:2455-7749
2455-7749
DOI:10.33889/IJMEMS.2019.4.4-084