A Novel Technique for Numerical Approximation of 2 Dimensional Non-Linear Coupled Burgers’ Equations using Uniform Algebraic Hyperbolic (UAH) Tension B-Spline based Differential Quadrature Method

Authors

Varun Joshi, Department of Mathematics, Lovely Professional University, Punjab, IndiaFollow
Mamta Kapoor, Department of Mathematics, Lovely Professional University, Punjab, IndiaFollow

Author Country (or Countries)

India

Abstract

AUniformAlgebraicHyperbolic(UAH)tensionB-splineoffourthorderbasedDifferentialquadraturemethodisdeveloped to tackle the non-linear coupled 2D Burgers’ equation, to fetch the weighting coefficients, used in differential quadrature method, UAH tension B-spline is used as the basis function. UAH tension B-spline based DQM is implemented in the case of spatial discretization and in time discretization, SSP-RK 43 scheme has been implemented. By employing the developed technique upon the coupled 2D non-linear Burgers’ equation, system of ODE got obtained, it is solved using SSP-RK43 scheme. In the present paper five numerical examples are tested to check the accuracy and efficiency of the developed scheme. A comparison is given in the form of L2 and L∞ error norms with the existing numerical schemes. Accuracy and effectiveness of developed scheme is shown in the form of tables and figures, as well. Stability of the present scheme is also tested by employing the matrix stability analysis method, which triggered the point that the developed scheme is unconditionally stable.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/150215

Recommended Citation

Joshi, Varun and Kapoor, Mamta (2021) "A Novel Technique for Numerical Approximation of 2 Dimensional Non-Linear Coupled Burgers’ Equations using Uniform Algebraic Hyperbolic (UAH) Tension B-Spline based Differential Quadrature Method," Applied Mathematics & Information Sciences: Vol. 15: Iss. 2, Article 15.
DOI: http://dx.doi.org/10.18576/amis/150215
Available at: https://digitalcommons.aaru.edu.jo/amis/vol15/iss2/15