In the present work, q-homotopy analysis transform method (q-HATM) was used to generate an analytical solution for moisture content distribution in a one-dimensional vertical groundwater recharge problem. Three scenarios Brooks–Corey model are studied based on linear and nonlinear diffusivity conductivity functions. The governing fractional partial differential equations solved effectively by c...

In this paper, the Kadomtsev-Petviashvili equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed...

In this research, three numerical methods, namely the variational iteration method, Adomian decomposition and homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from classical (FW) by replacing integer-order time derivative with Caputo fractional of order η=(0,1] variable co...

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 ...

This paper is devoted to the study of relation between `formal exponential maps,' Atiyah class, and Kapranov $L_\infty[1]$ algebras associated with dg manifolds in $C^\infty$ context. Given a manifold, we prove that map' exists if only class vanishes. Inspired by Kapranov's construction homotopy Lie algebra holomorphic tangent bundle complex space vector fields on manifold admits an structure, ...

The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and ill-conditioned Jacobian matrices encountered in tracing of homotopy paths affect the numerical stability. We present modified homotopy functions with a new homotop...

We compare Friedlander’s definition of étale homotopy for simplicial schemes to another definition involving homotopy colimits of pro-simplicial sets. This can be expressed as a notion of hypercover descent for étale homotopy. We use this result to construct a homotopy invariant functor from the category of simplicial presheaves on the étale site of schemes over S to the category of pro-spaces....