Numerical solution of the controlled Duffing oscillator by semi-orthogonal spline wavelets

Numerical Solution of the Controlled Harmonic Oscillator by Homotopy Perturbation Method

‎The controlled harmonic oscillator with retarded damping‎, ‎is an important class of optimal control problems which has an important role in oscillating phenomena in nonlinear engineering systems‎. ‎In this paper‎, ‎to solve this problem‎, ‎we presented an analytical method‎. ‎This approach is based on the homotopy perturbation method‎. ‎The solution procedure becomes easier‎, ‎simpler and mor...

Efficient Solution of Nonlinear Duffing Oscillator

In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicabil...

numerical solution of damped forced oscillator problem using haar wavelets

we present here the numerical solution of damped forced oscillator problem using haar wavelet and compare the numerical results obtained with some well-known numerical methods such as runge-kutta fourth order classical and taylor series methods. numerical results show that the present haar wavelet method gives more accurate approximations than above said numerical methods.

Numerical solution of the forced Duffing equations‎ ‎ using Legendre multiwavelets

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

The solution of a second-order nonlinear differential equation with Neumann boundary conditions using semi-orthogonal B-spline wavelets