As one of themost important subjects of mathematics, differential and integral equations are widely used to model a variety of physical problems. Perturbation methods have been used in search of approximate analytical solutions for over a century [1–3]. Algebraic equations, integral-differential equations, and difference equations could be solved by these techniques approximately. However, a ma...

In this paper, we apply the variational iteration method using He’s polynomials for finding the analytical solution of gas dynamic equation. The proposed method is an elegant combination of He’s variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in such problems. The proposed iterative scheme finds the s...

In this paper, we present a comparative analysis of non-reactive contaminant flow problem for constant initial concentration in two dimensions by homotopy-perturbation and Variational Iteration method. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically by homotopy-perturbation method (HPM) and Variational...

In this paper, we consider the variational homotopy perturbation method (VHPM) to obtain an approximate series solution for the generalized Fisher’s equation which converges to the exact solution in the region of convergence. Comparisons are made among the variational iteration method (VIM), the exact solutions and the proposed method. The results reveal that the proposed method is very effectiv...

analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. according to this, an impressive analytical method which is called modified iteration perturbation method (mipm) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. this new method is combined by the mickens and iteration methods. moreover, this method don...

We present an improved version of a full Nesterov-Todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (Bull. Iranian Math. Soc., 40(3), 541-564, (2014)). In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new...

the purpose of this study is to compare the results of different probabilistic methods such as the perturbation method, stochastic finite element method (sfem) and monte carlo method. these methods were used to study the convergence of direct approach for slope stability analysis and are developed for a linear soil behavior. in this study, two dimensional random fields are used and both the fir...

In the paper, a modification of rendering algorithm of polynomiograph is presented. Polynomiography is a method of visualization of complex polynomial root finding process and it has applications among other things in aesthetic pattern generation. The proposed modification is based on a perturbation mapping, which is added in the iteration process of the root finding method. The use of the pert...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method VHPM . We use this method for solving higher dimensional initial boundary value problemswith variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these prob...