Abstract: In this article, we propose a reliable combination of Homotopy analysis method (HAM) and Laplace decomposition method (LDM) to solve linear and nonlinear partial differential equations effectively with less computation. The proposed method is called homotopy analysis transform method (HATM). This study represents significant features of HATM and its capability of handling linear and n...

Specific competencies for the project 25 years of research experience in nonlinear partial differential equations; Extensive photographic skills (see http://pbase.com/markowich); Wittgenstein Award of the Austrian Research Fund (FWF) 2000; Corresponding Member of the Austrian Academy of Sciences since 2005; Coordination and participation in Austrian and international grants and network projects...

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. E...

This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE) together with solutions parameterized by the set of arbitrary functions.

sufficient conditions are established under which the zero solution x = 0 of equation (2) isunstable.

in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...