A new approximate analytical method for solving some non-linear initial value problems in physical sciences
Abstract
In this research study, one new approximate analytical method called Ananthaswamy-Sivasankari method for initial value problems is used to obtain the approximate solutions to some physical science problems, especially oscillator with fractional nonlinearities, duffing-harmonic oscillator, Helmholtz equation and some non-linear differential equations of oscillator analytically. The numerical and analytical solutions to these equations are then compared and the results indicate a good agreement. The explicit and closed form of derived approximate analytical solutions is given. The results explained that the new method is more convenient and easy to solve. Moreover, the outcomes are interlined graphically.