Taylor wavelet collocation method for Benjamin–Bona–Mahony partial differential equations

Abstract

In this paper, we have developed a computational method for solving Benjamin–Bona–Mahony (BBM) partial differential equations which is based on the Taylor wavelets with the collocation technique. And applying the convergence analysis, convergence and error analysis of the proposed technique of Taylor wavelets is worked out and it is shown to converge uniformly on it. We derive numerical solutions to BBM equations with various parameters using the Taylor wavelet collocation method (TWCM). And also the obtained TWCM based numerical solutions have been compared with the analytical solutions and existing methods of solutions (Shiralashetti et al., 2016; Rahana et al., 2019 and Hariharan, 2014). The error analysis in the obtained solutions shows the competence and consistency of the proposed method. It is predicted that the proposed method can be set up expansively and appropriate for the solution of a diverse classes of nonlinear partial differential equations arising in science and engineering.