In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

The problem of the peakon and antipeakon solutions Novikov equation including term ωux is studied. It well known that, when ω=0, admits solutions. In this study, it shown via homotopy analysis method even in case where ω≠0, also

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting these (co)limits and that they are preserved by the functors in the limit cone. In particular, the BousfieldKan homotopy limit of a diagram of quasi-categori...

This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the square residual error, the optimal convergence-control parameters ...

in this paper, the homotopy perturbation method (hpm) and elzaki transform is employed to obtain the approximate analytical solution of the sine gorden and the klein gorden equations. the nonlinear terms can be handled by the use of homotopy perturbation method. the proposed homotopy perturbation method is applied to reformulate the first and the second order initial value problems which leads ...

In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integrodifferential equation by using the following powerful, efficient but simple methods: (i) Modified Adomian decomposition method (MADM), (ii) Variational iteration method (VIM), (iii) Homotopy analysis method (HAM) and (iv) Modified homotopy perturbation method (MHPM). The uniqueness of the solution and the conve...

In this paper, an algorithm based on the collocation and homotopy analysis methods, for solving initial-boundary value problems, is introduced. The application of this algorithm is based on the approximation and interpolation of the dependent variables by using suitable functions or polynomials according to their values in the collocation points corresponding to a suitable discretization of the...