This paper, presents a relatively new approach to solve second order one dimensional non-linear wave equation. We use modified cubic B-spline basis functions based differential quadrature method for space discretization, which gives results in an amenable system of differential equations. The resulting system of equations has been solved using SSP-RK43 scheme. The SSP-RK43 scheme needs less storage space and causes less accumulation of numerical errors. The utility of the scheme is that it does not need any linearization or transformation for handling the non-linear terms and hence reduces the computational effort. The accuracy of the approach has been confirmed with numerical experiments. L2 and L∞ error norms are computed for each example and it is shown that the results obtained are acceptable and are in good agreement with the earlier studies. © 2014 IEEE.