<p>This article focuses on solving the Gardner equation through two numerical schemes that use the differential quadrature method (DQM) with modified quintic B-spline as basis functions. The equation has numerous applications in quantum field theory, hydrodynamics, plasma physics and other fields. The first numerical scheme uses the Crank-Nicolson and forward finite difference techniques for discretization, and the Rubin and Graves method to linearize the equation’s nonlinearity. Then, the modified DQM is applied to the spatial derivatives, yielding a system of linear equations. In the second numerical scheme, the Gardner equation is directly discretized using the DQM and converted into a system of ordinary differential equations (ODEs), which are then solved with the strong stability preserving Runge-Kutta method (SSP-RK43). The stability of both schemes is also discussed, and they are discovered to be unconditionally stable. The efficacy of these approaches is assessed by numerical experiments on four examples. The outcomes are shown arithmetically and graphically to prove the accuracy of the proposed numerical schemes. A comparative analysis is performed between two proposed numerical schemes and also with those previously reported results in the literature. The findings suggest that the second scheme performs better than the first scheme. The proposed strategies are simple to comprehend and effective.</p>