A novel technique for numerical approximation of 1D non-linear coupled Burgers' equation by using cubic Hyperbolic B-spline based Differential quadrature method

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Mamta Kapoor, Varun Joshi

Abstract

In this paper, a novel scheme, cubic Hyperbolic B-spline-based Differential Quadrature Method,
is proposed for the solution of 1D non-linear viscous coupled Burgers' equation. The numerical
approximation of this mentioned equation is obtained by using the Hyperbolic B-spline-based
Differential quadrature method. Hyperbolic B-spline is used as a basis function in DQM in order
to obtain weighting coefficients, then received a set of ODEs is solved by using Strong Stability
Preserving Runge Kutta-43 scheme(SSP-RK43 scheme). The accuracy and effectiveness of this
proposed scheme are tested by using three examples. The obtained results are matched with the
previous results present in the literature of other methods as well as with the exact solutions by
means of

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