New cubic B-spline approximation technique for numerical solutions of coupled viscous Burgers equations

Abstract

Purpose The purpose of this paper is to present a new cubic B-spline (CBS) approximation technique for the numerical treatment of coupled viscous Burgers’ equations arising in the study of fluid dynamics, continuous stochastic processes, acoustic transmissions and aerofoil flow theory. Design/methodology/approach The system of partial differential equations is discretized in time direction using the finite difference formulation, and the new CBS approximations have been used to interpolate the solution curves in the spatial direction. The theoretical estimation of stability and uniform convergence of the proposed numerical algorithm has been derived rigorously. Findings A different scheme based on the new approximation in CBS functions is proposed which is quite different from the existing methods developed (Mittal and Jiwari, 2012; Mittal and Arora, 2011; Mittal and Tripathi, 2014; Raslan et al., 2017; Shallal et al., 2019). Some numerical examples are presented to validate the performance and accuracy of the proposed technique. The simulation results have guaranteed the superior performance of the presented algorithm over the existing numerical techniques on approximate solutions of coupled viscous Burgers’ equations. Originality/value The current approach based on new CBS approximations is novel for the numerical study of coupled Burgers’ equations, and as far as we are aware, it has never been used for this purpose before.

Numerical solution of the coupled Burgers equation by trigonometric B‐spline collocation method

“…The author has concluded that a suitable optimal of the initial condition leads towards the vital exact solution after some iterative phases. Nazir et al 25 presented a new cubic B‐spline (CBS) approximation technique for the numerical treatment of coupled viscous Burgers equations arising in the study of fluid dynamics, continuous stochastic processes, acoustic transmissions and aerofoil flow theory. The authors have discretized the system of partial differential equations in time direction using the finite difference formulation, and they have used the new CBS approximations to interpolate the solution curves in the spatial direction.…”

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