Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...

This paper presents an approximate approach to analysis of spacetime structures for unsteady problems in CFD (computational fluid dynamics). The approach is based on the solution of optimization problem combined with methods of data visual presentation. This approach is intended for fast approximate estimation of unsteady flow structures dependence on character parameters (or determining parame...

Approximate analytical methods have been used extensively for finding approximate solutions to nonlinear ordinary differential equations. In this paper we compare the recently developed direct normal form transformation with two other very well known and long standing methods, harmonic balance and the method of multiple scales. We will show that the direct normal form method combines some of th...

Queueing networks with finite capacity queues and blocking are applied to model systems with finite resources and population constraints, such as computer and communication systems, as well as traffic, production and manufacturing systems. Various blocking types can be defined to represent different system behaviors. When a customer attempts to enter a full capacity queue blocking occurs. The a...

The initial and boundary value problem in enzyme reactions mechanism for inhabitation process is discussed. Approximate analytical expressions for the concentrations of substrate and product are presented. Approximate analytical solutions of non-linear reaction equations containing non-linear terms related to enzymatic reaction mechanism are solved using Homotopy perturbation method. The releva...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

In this paper, we construct an analytical solution of the coupled Burgers’ equation, using homotopy analysis method, which is a semi-analytical approximate obtained by method convergent for different values convergence control parameter ℏ, optimal value ℏ corresponding with minimum error to be determined residual. The results present are compared other solutions numerical methods.