Hermite wavelet method for solving nonlinear Rosenau–Hyman equation

Abstract

In this paper, we present an approximate solution for solving the nonlinear Rosenau–Hyman equation. The method is based on adapting the wavelet technique accompanied with the Hermit polynomials. Convergence analysis for the proposed method is being investigated, proving that the Hermite wavelet expansion is uniformly convergent. A test example is presented for different values of the parameters, and the obtained results are compared to other relevant methods from the literature. The process proves to have the ability to produce accurate results than the other compared methods. Some graphical representations for the problem are drawn to illustrate the behavior of the solution.

Keywords

• Hermite wavelets
• Operational matrix of integration
• Collocation method