Mathematical methods in solving nonlinear differential equations

Several methods are used for solving the differential equations. All of these methods are known providing solutions to the problems. Many researchers have been solving these problems by using the known techniques such as modified Differential Transform Method Homotopy Perturbation Method Sumudu Transform series Decomposition Method and so on for many years. All these methods provide solutions that are good agreement with the exact solutions. For the case of truly nonlinear differential equations oscillatory perturbation the standard classical procedures are not able to provide the solutions. In this study the standard equations of a ball bearing oscillating in a U-shaped tube and the equation of an ear drum (which is also known as Helmholtz equation of motion) are used as a case study to validate the accuracy of the some well known Modified methods like differential transform method Homotopy perturbation method Sumudu transform series decomposition method.