Numerical Solution of the Gardner Equation - Tiong, W.K.; Tay, K.G.; Ong, C.T.; Sze, S.N. (2016)
The Gardner equation is commonly used to describe wave propagation in weakly nonlinear dispersive medium. The Gardner equation has a higher order nonlinear term, which could make the numerical calculation inaccurate. In this paper, the Gardner equation is solved using two numerical methods, i.e., the method of lines and pseudospectral method. The efficiency and accuracy of both methods were studied. Our results show that both methods are accurate and efficient methods to solve the Gardner equation. By comparing the accuracy of both the methods, the method of lines performs better than pseudospectral method most of the time.