Abstract
In this article, an initial and boundary value problem for variable coefficients coupled KdV-Burgers equation is considered. With the help of Lie group approach, initial and boundary value problem for variable coefficients coupled KdV-Burgers equation reduced to an initial value problem for nonlinear third-order ordinary differential equations (ODEs). Moreover, the systems of ODEs are solved to obtain soliton solutions. Further, classical fourth-order Runge-Kutta method is applied to systems of ODEs for constructing numerical solutions of coupled KdV-Burgers equation. Numerical solutions are computed, and accuracy of numerical scheme is assessed by applying the scheme half mesh principal to calculate maximum errors.