An analytical approximation for coupled viscous Burgers’ equation

Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

The coupled viscous Burgers’ equation which was derived by Esipov in 1995 to study the model of poly-dispersive sedimentation. The system of coupled viscous Burgers’ equation is a simple model of sedimentation or evolution of scaled volume concentrations of two kinds of particles in fluid suspensions or colloids under the effect of gravity. Coupled Burgers’ equation can be written in the follow...

An Explicit Solution of Coupled Viscous Burgers’ Equation by the Decomposition Method

We consider a coupled system of viscous Burgers’ equations with appropriate initial values using the decomposition method. In this method, the solution is calculated in the form of a convergent power series with easily computable components. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The decomposition series solution of the problem is quickly o...

Reduced Basis Approximation and A Posteriori Error Estimation for the Time-Dependent Viscous Burgers Equation

In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution–dependent (Online) calculation of the exponential–in–time stability factor by the Successive Constraint Method. Numerical results indicate that the a posteriori error bounds are practicable fo...

An H-Galerkin mixed method for the coupled Burgers equation

In this paper, an H-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived. Keywords—The coupled Burgers equation; H-Galerkin mixed finite element method; Backward Euler’s method; Optimal error estimates.

Discrete Approximation of the Riemann Problem for the Viscous Burgers Equation