A 3-Scale Haar Wavelet Collocation Method for Numerical Solution of the Nonlinear Gardner Equation

Abstract In this paper, a 3-scale Haar wavelet collocation method was applied to the nonlinear Gardner equation which can be used to describe the large-amplitude inner waves in the ocean. We start the solution process with the time discretization of the Gardner equation, with the help of finite difference method. Then, we have used 3-scale Haar wavelets for the space discretization. These steps gave us a system of algebraic equations, by solving these equations we were able to get wavelet coefficients and used them to construct the numerical solution of the Gardner equation. We applied the proposed method to five different problems to test the accuracy and compared the obtained results with other studies in the literature. The results and comparisons are given in tables and solutions are depicted graphically. The results show that the method proposed in this manuscript is highly accurate even with a low number of collocation points.