Numerical solution of the coupled viscous Burgers’ equation

A Reproducing Kernel Method for Solving a Class of Nonlinear Systems of Pdes

“…The norm infinity, norm of relative errors, and CPU time of the method for the numerical solution of u are tabulated in Table 1 at different time T = 0.1, 0.5, 1. It can be noted from Table 1 that the accuracy of the proposed method are in agreement with [10] and [18]. Numerical solutions of u are also depicted in Figure 1.…”

“…The method is mesh free, easily implemented and capable in treating various boundary conditions. The method needs no time discretization against [7,10] and any ODE integrator against [5,9,18]. Therefore there is no concern about the stability problem and also increasing the end of time T does not increase the CPU time.…”

“…Many authors have studied the analytical and approximate solutions of nonlinear systems of PDEs by using various techniques. Some of them are the methods of exp-function [13], Chebyshev spectral collocation [9], radial basis functions collocation [7], compactly supported radial basis functions collocation [20], Chebyshev pseudospectral multidomain [5], cubic B-spline collocation [10], and Fourier pseudospectral [18].…”

Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

“…In [21], another set of CBEs has been considered. Author of [17] has gained the multiple kink and singular kink solutions of (7) under the constraint u(ε, τ) = v(ε, τ).…”

“…(ii) As a generalized model in fluid dynamics, the coupled Burgers-type equations (CBEs) [17,20,21] may describe certain phenomena, e.g., the sedimentation or evolution of scaled volume concentrations of two kinds of particles in fluid suspensions or colloids under the effect of gravity. The CBEs can be written as [20] …”