in recent years, numerous approaches have been applied for finding the solutions of functional equations. one of them is the optimal homotopy asymptotic method. in current paper, this method has been applied for obtaining the approximate solution of fisher equation. the reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

Boyd, J.P., A comparison of numerical and analytical methods for the reduced wave equation with multiple spatial scales, Applied Numerical Mathematics 7 (1991) 453-479. We compare four different techniques for solving the ordinary differential equation u,, + u = I on the unbounded interval, x E [ 00, co], when f( EX) decays rapidly as ) x ( + co. This problem, although very simple, is represent...

A perturbation algorithm using any time transformation is introduced. To account for the nonlinear dependence of the function, we exhibit the function f of the system in the differential equation. To this end, we introduce the transformation t t w f Te ) , ( , where f is a function that depends on t or w. The problems are solved with new time transformation: Linear damped vibration equation, cl...

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

Abstract Quasi-periodic (QP) solutions of a damped nonlinear QP Mathieu equation with cubic nonlinearity are investigated by using the incremental harmonic balance (IHB) method two time scales. The contains incommensurate excitation frequencies, one is small frequency while other nearly equals twice linear natural frequency. It found that Fourier spectra consist uniformly spaced sidebands due t...

the dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and poincar'{e} sections. also, we employed perturbation methods such as lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.