Numerical analysis via Chebyshev pseudospectral method for nonlinear initial/boundary value problems

Abstract

In applied science, the physical models are usually described by nonlinear initial/boundary value problems. The exact solutions for such nonlinear models are not always available, the reason that many authors resort to the numerical methods. One of these numerical methods is the Chebyshev pseudospectral method. This method is applied in the current paper to solve some nonlinear initial and boundary value problems of particular interest in applied sciences and engineering. In order to explore the effectiveness and the validity of the present method, many physical models of nonlinear type such as generalized nonlinear oscillator, relativistic oscillator, and Bratu's equations have been solved numerically. The obtained results are compared with other published works through tables and graphs where good accuracy has been achieved.