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Recently solving integro-differential equations have been the focus of attention among many researchers in the field of mathematic and engineering. The aim of current study is to apply the well-known optimal homotopy asymptotic method (OHAM) on a specific and famous model of these equations. It is illustrated that auxiliary functions and the number of Taylor series terms affect the accuracy of the solution. Hence, at first a solution has been found with an acceptable error by OHAM. Then, it has been continued to attain a better solution by Multistep optimal homotopy asymptotic method. All these processes had improved the precision of the solution. Auxiliary polynomials of two, three, and four degrees and different numbers of Taylor series term have been investigated to solve a nonlinear system derived by two biological species ‎living together. Ultimately, appropriate results with auxiliary polynomials of degree four and Taylor series with six terms have been obtained precisely. In addition, the error values decrease significantly compared to the other cases.

In the present paper, a modified simple equation method is used to obtain exact solutions of the equal width wave Burgers and modified equal width wave Burgers equations. By giving specific values to the parameters, particular solutions are obtained and the plots of solutions are drawn. It shows that the proposed method can be easily generalized to solve a variety of non-linear equations by implementing a robust and straightforward algorithm without the need for any tools. [ABSTRACT FROM AUTHOR]

In this study, the asymptotic Adomian decomposition method (AADM) is implemented to solve fractional order Riccati differential equations. The product integration method is used to solve the singular integrals, resulted from fractional derivative. Some fractional order Riccati differential equations are presented as examples to illustrate the ability and effciency of the proposed approach. The approximate solutions of AADM are compared with the results of the Laplace Adomian Pade method (LAPM). Generalizing AADM for solving fractional Riccati differential equations by the far-field approximation indicates the novelty of the paper. [ABSTRACT FROM AUTHOR]

There are some methods to obtain approximate solutions of functional equations. One of them is the homotopy perturbation method. However, computing coefficients of pj, is time-consuming and challenging. In order to deal with this problem, a new modified homotopy perturbation method is introduced, which doesn't need computations of the coefficients of pj. Here, the method has been applied to solve some examples and the results have been compared with those obtained from the homotopy perturbation method. Moreover, convergence of the method has been discussed. [ABSTRACT FROM AUTHOR]

In this paper, G′/G-expansion and tanh-methods, as two well known methods, for solving partial differential equations are compared. It has been shown that these two methods are the same, for solving partial Differential equation in special conditions. For illustration and more explanation of the idea, two examples are provided. [ABSTRACT FROM AUTHOR]

In this paper, the fractional-order differential model of HIV-1 infection of CD4+ T-cells with the effect of drug therapy has been introduced. There are three components: uninfected CD4+ T-cells,x , infected CD4+ T-cells,y , and density of virions in plasma,z . The aim is to gain numerical solution of this fractional-order HIV-1 model by Laplace Adomian decomposition method (LADM). The solution of the proposed model has been achieved in a series form. Moreover, to illustrate the ability and efficiency of the proposed approach, the solution will be compared with the solutions of some other numerical methods. The Caputo sense has been used for fractional derivatives. [ABSTRACT FROM AUTHOR]