Global solution of the critical Burgers equation in N Dimensions

Ru, Shaolei; Chen, Jiecheng

doi:10.1016/j.camwa.2017.04.022

Cited by 2 publications

(2 citation statements)

References 28 publications

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“…Bhatt and Khaliq (2016) developed two fourth-order time differencing schemes for the numerical solution of nonlinear Burgers' equations. Ru and Chen (2017) studied the global solutions of the critical Burgers' equation in n-dimensions. He and Tang (2016) used the lattice Boltzmann method for the numerical simulation of CVBEs.…”

Section: Introductionmentioning

confidence: 99%

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

Nazir

Abbas

Iqbal

2020

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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.

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Section: Introductionmentioning

confidence: 99%

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

Nazir

Abbas

Iqbal

2020

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“…The Burgers' equations, and an associated family of equations, have garnered considerable attention in recent years, in terms of numerical simulations, analytic methods of solution , analysis as well as physical interpretation of the equation dynamics. Klein and Saut present a numerical study of the Burgers' equation identifying blow‐up mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Numeric solution of advection–diffusion equations by a discrete time random walk scheme

Angstmann

Henry

Jacobs

et al. 2019

Numerical Methods Partial

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Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups, and discontinuities. Here we present an explicit numerical scheme for solving nonlinear advection–diffusion equations admitting shock solutions that is both easy to implement and stable. The numerical scheme is obtained by considering the continuum limit of a discrete time and space stochastic process for nonlinear advection–diffusion. The stochastic process is well posed and this guarantees the stability of the scheme. Several examples are provided to highlight the importance of the formulation of the stochastic process in obtaining a stable and accurate numerical scheme.

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Global solution of the critical Burgers equation in N Dimensions

Cited by 2 publications

References 28 publications

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

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

Numeric solution of advection–diffusion equations by a discrete time random walk scheme

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