A fast and efficient scheme for solving a class of nonlinear Lienard’s equations

Abstract

In this work, we propose a numerical framework for solving a class of Lienard’s equation. This equation arises in the development of radio and vacuum tube technology. The spatial approximation is based on the Bernoulli collocation method in which the shifted Chebyshev collocation points are used as collocation nodes. The operational matrix of derivatives of Bernoulli is introduced. The matrix together with the collocation method is then utilized to reduce the problem into a system of nonlinear algebraic equations. Also, a reliable and fast approach for solving this nonlinear system is discussed. The error function is presented to assure the accuracy of the solution. Numerical results and comparisons with other existing methods provided in the literature are made proving the ability of the proposed scheme of providing excellent results.