A class of bivariate infinite series solutions the elliptic and hyperbolic Kepler equations is described, adding to handful 1-D that have been found throughout centuries. This result based on an iterative procedure for analytical computation all higher-order partial derivatives eccentric anomaly with respect eccentricity e mean M in a given base point (ec,Mc) (e,M) plane. Explicit examples such...

Based on homotopy, which is a basic concept in topology, a general analytic method (namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear differential equations. Different from perturbation techniques, this approach is independent of small/large physical parameters. Besides, different from all previous analytic methods, it provides us with a simple way to adju...

Power systems are subjected to small–signal oscillations that can be caused by sudden change in the value of large loads. To avoid the dangers of these oscillations, the Power System Stabilizers (PSSs) are used. When the PSSs can not be effective enough, installation of the Thyristor–based compensators to increase the oscillations damping is a suitable method. In this paper, a Static Synchronou...

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite ...

analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

‎linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎in this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎by a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎then‎, ‎we use...