Integrated Chebyshev wavelets for numerical solution of nonlinear one-dimensional and two-dimensional Rosenau equations

In this study, we focus on developing an efficient computational method for one-dimensional and two-dimensional nonlinear Rosenau equations. Suggested computational method in this study uses finite differences for discretization of time variable. For discretization of space variables, firstly unknown function with highest derivative which is appeared in the Rosenau equation is expanded to Chebyshev wavelets and then by successive integrations the unknown function itself is found in terms of truncated Chebyshev wavelets. Also, a linearization technique is applied to handle the nonlinearity. By doing so we obtain a linear system of equations for solving the Rosenau equation. We apply the suggested method to four test problems and compare obtained numerical solutions with exact solutions and with finite element method to assess how accurate are the numerical results. The obtained numerical results endorse the efficiency and practicality of the suggested method for both one-dimensional and two-dimensional nonlinear Rosenau equations.