A new numerical technique to seek properties of the nonlinear oscillators

Numerical methods are widely used in the area of nonlinear problems including differential equations. There are various integral transformations to study the frequency formulations and nonlinear solutions, but there are many types of transformations that make it difficult to choose during use. Recently, Professor He proposed a general integral transformation, which is a generalization of the Laplace transform, Fourier transform, and other transformations existing in the literature. The unification can provide more opportunities for expanding research on physical phenomena and engineering problems. This new transformation coupled with the variational iteration method is highly effective for various nonlinear problems and offers a new window for wide applications. A new scheme of correction functional is obtained and a numerical example is taken to support the primary findings. The Lagrange multiplier is easily obtained and an algorithm is developed. Taking an oscillator with coordinate-dependent mass as an example to illustrate that the approximate solution is quickly obtained by the final algorithm. A high approximate nonlinear frequency and the solution are solved and the graphical representation is given. It will be a challenge and future trend for the nonlinear research.