The Galerkin Method for Solving Strongly Nonlinear Oscillators

In this paper, we make use of the Galerkin method for solving nonlinear second-order ODEs that are related to some strongly nonlinear oscillators arising in physics and engineering. We derive the iterative schemes for finding the coefficients that appear in the linear Galerkin hat combination in the ansatz form solution. These coefficients may be found iteratively by solving either a quadratic or a higher degree algebraic equation. Examples are presented to illustrate the obtained results. Some exact solutions are given, and they are compared with both the Runge–Kutta numerical solution and the solution obtained using the Galerkin finite element method.