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In the present paper, a Barycentric Lagrange interpolation polynomial-based Differential quadrature method is applied to get the numerical solution of non-linear coupled 2D But-gers' equation, For this process, first of all, the coupled Burgers' equation is dealt with generalized formula, By using the obtained generalized formula, required weighting coefficients in the differential quadrature method are easily calculated, Afterward, the reduced set of ordinary differential equations is solved by using the SSP-RK43 scheme, To test the efficiency of the newly applied method, the L., error norm has been computed, To test the stability of the proposed method, the Matrix stability analysis method is implemented, which shows that the developed method is unconditionally stable. [ABSTRACT FROM AUTHOR]

In this work, a numerical regime based upon the Non-Uniform Algebraic Hyperbolic Bspline is developed with the aid of the differential quadrature method named NUAH B-spline DQM to fetch the numerical approximation of non-linear coupled ZD Burgers equation. In the first step, the spatial discretization is mentioned using the NUAH B-spline of order 4: for improvised results, modified formulae are implemented, In the second step, the reduced system of ordinary differential equations is dealt using SSP-RK43 regime. The proposed regime is analyzed for stability also. Finally, the effectiveness and adaptability of the proposed regime are confirmed with the aid of numerical experiments, and fetched results are compared with the existing outcomes in the literature. It is observed that the present scheme is unconditionally stable by implementing the concept of the matrix stability analysis method. It is found that the present regime is easy to implement and produces accurate results. [ABSTRACT FROM AUTHOR]

In this paper, a novel approach named Uniform Algebraic Hyperbolic (UAH) tension Bspline Differential quadrature me thod is implemented for the numerical approximation of 1 D Burgers' equation. In this work. UAH tension B-spline basis function is used for the spatial discretization. After finding the weighting coefficients. the original system is reduced to the system of ordinary differential equations, when SSP-RK 43 scheme is implemented. Accuracy of the present method is validated via & and l* error norms. Present results are compared with existing results and these results are acceptable. [ABSTRACT FROM AUTHOR]

In this, research work. we present a novel technique named Hyperbolic B-spline based Differential quadrature method to get the numerical approximations of the 1 D and 2D coupled nonlinear Schrodinger equations. The coupled non-linear Schrodinger equation represents the range of physical phenomena with the aid of a model equation for the optical fiber with the linear birefringence. In present paper. Differential quadrature method is applied over the mentioned PDEs and reduced set of ordinary differential equations is solved by SSP-RK43 scheme. Accuracy and effectiveness of the proposed scheme is checked by L∞ error norm and conservation of mass properly is also tested. In present paper. elastic property is also checked. whether the wave amplitudes have restored their shapes or not for the different used parameters and stability of the proposed scheme is checked via matrix stability analysis method. which indicates that the present method has the property of unconditionally stable. [ABSTRACT FROM AUTHOR]