Analytic Approximation Of Solutions Research Articles

The HAM Solutions for Unsteady Boundary Layer Flow and Heat Transfer with Heat Source/Sink

Considering the combined effects of the magnetic field and viscous dissipation, this paper investigates the problem of two-dimensional incompressible unsteady flow over a horizontal continuous stretching sheet. Due to the strongly nonlinear and various parameters of this problem, the governing boundary layer equations are transformed into a system of nonlinear differential equations through the similarity transformation, and then analytical approximations of solutions are derived by homotopy analysis method. In addition, the effects of physical factors on the flow and heat transfer characteristics are examed and discussed graphically.

Research on Fluid Mechanics with Slip Flow of Viscoelastic Fluid in the Micro Channel

Stagnation flow, an import research branch of fluid mechanics, describing the fluid motion near the stagnation region, exists on all solid bodies moving in a fluid. And stagnation point boundary layer flow problems described by partial differential equations have attracted many scholars attention nowadays. These problems have become difficult and hot in the study of applied mathematics, mechanics and materials engineering. This paper has transformed the governing boundary layer equations into a system of nonlinear differential equations through the similarity transformation, and the analytical approximations of solutions are derived by homotopy analysis method (HAM). In addition, the effects of physical factors (such as the slip parameter, Magnetic field parameter and Reynolds number) on the flow are examed and discussed graphically. They have a great impact on the speed.

Maxwell Fluids Unsteady Mixed Flow and Radiation Heat Transfer Over a Stretching Permeable Plate With Boundary Slip and Nonuniform Heat Source/Sink

This paper presents an analysis for the unsteady mixed boundary-layer flow and radiation heat transfer of generalized Maxwell fluids toward an unsteady stretching permeable surface in presence of boundary slip and nonuniform heat source/sink. The governing partial differential equations are converted into nonlinear ordinary differential equations and analytical approximations of solutions are derived by homotopy analysis method (HAM). The effects of the unsteadiness parameter, nonuniform heat source/sink parameter, suction/injection parameter, thermal radiation parameter and slip parameter on the fluid flow, and heat transfer characteristics are shown graphically and analyzed.

Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

Analytic approximation of solutions of differential equations

Mathematical software such as Macsyma, Mathematica, and Maple have built in differential equation solvers and Taylor series procedures for solving a wide variety of differential equations with associated conditions. If one selects examples that do not fit in with the assumptions used in these solvers, then one must develop alternative programs to approximate solutions with this software. In this paper, we employ iterative methods along with various Gronwall inequalities to obtain high order approximations of solutions for an extensive variety of such examples by means of Maple programs. The types of problems considered include initial value problems for singular and mixed linear–nonlinear equations. Plots of an number of approximate solutions are given and the Maple programs employed are appended at the end of the paper.

On the propagation of error in air pollution measurements

Four methods for estimating the uncertainties in air pollution measurements are outlined. The approaches are: analytical solution-approximation; application of distribution theory; experimentation; and simulation. The advantages and disadvantages of each method are illustrated using data from High-Volume air samplers, the instrument most commonly used for monitoring ambient concentrations of airborne particles.