In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method. The efficiency and accuracy of the present method is demonstrated by two aspects. One is analyzing the approximate solutions graphically. The other is compari...

Abstract: In this work, we consider special problem consisting of twelfth order two-point boundary value by using the Optimal Homotopy Asymptotic Method (OHAM). The proposed method has been thoroughly tested on problems of all kinds and shows very accurate results . Furthermore, we also compared the results obtained from this technique with the available exact solution in different literatures....

The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the h...

In this paper, Optimal Homotopy Asymptotic Method (OHAM) is combined with Galerkin method to investigate the MHD Jeffery-Hamel flows in non-parallel walls for strongly nonlinear ordinary differential equations. Results for velocity profiles in divergent and convergent channels for various values of Hartmann and Reynolds numbers are compared with numerical method (the Runge-Kutta method of order...

Aim of the paper is to investigate approximate analytical solution of time-dependent partial differential equation using a semi-analytical method, the Optimal Homotopy Asymptotic Method (OHAM). To show the efficiency of the proposed method, we consider one-dimensional heat and advection-diffusion equations. OHAM uses simple computations with pretty good enough approximate solution, which has an...

This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities, using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass, and quintic nonlinear beam are investigated to exhibit the reliability and ability of the p...

the statistical analysis of spatial data is usually done under gaussian assumption for the underlying random field model. when this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. one of the crucial problems in this setting is specifying the block sizes. in this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...