Approximate analytical solutions to nonlinear oscillations via semi-analytical method

Abstract

A modified algebraic method is proposed in this study as an effective semi-analytical method for obtaining analytical solutions for two types of nonlinear differential equations. The trial solution is assumed to be a polynomial, and the algebraic approach is used to find the unknown coefficients. To enhance the solution, first, we apply the Laplace transformation on the series solution and then create the Padé approximations of the resultant equation. Finally, for the nonlinear problems under discussion, the inverse Laplace transformation is used to obtain periodic solutions.

Keywords

• Modified algebraic method, circular sector oscillator
• Simple pendulum
• Nonlinear oscillators
• Numerical method