Abstract: The paper presents the design of a mini-UAV attitude
controller using the backstepping method. Starting from the nonlinear
dynamic equations of the mini-UAV, by using the backstepping
method, the author of this paper obtained the expressions of the
elevator, rudder and aileron deflections, which stabilize the UAV, at
each moment, to the desired values of the attitude angles. The attitude
controller controls the attitude angles, the angular rates, the angular
accelerations and other variables that describe the UAV longitudinal
and lateral motions. To design the nonlinear controller, by using the
backstepping technique, the nonlinear equations and the Lyapunov
analysis have been directly used. The designed controller has been
implemented in Matlab/Simulink environment and its effectiveness
has been tested with a campaign of numerical simulations using data
from the UAV flight tests. The obtained results are very good and
they are better than the ones found in previous works.
Abstract: In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.
Abstract: In the present paper some recommendations for the
use of software package “Mathematica" in a basic numerical analysis
course are presented. The methods which are covered in the course
include solution of systems of linear equations, nonlinear equations
and systems of nonlinear equations, numerical integration,
interpolation and solution of ordinary differential equations. A set of
individual assignments developed for the course covering all the
topics is discussed in detail.
Abstract: This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Abstract: In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.
Abstract: Based on Traub-s methods for solving nonlinear
equation f(x) = 0, we develop two families of third-order
methods for solving system of nonlinear equations F(x) = 0. The
families include well-known existing methods as special cases.
The stability is corroborated by numerical results. Comparison
with well-known methods shows that the present methods are
robust. These higher order methods may be very useful in the
numerical applications requiring high precision in their computations
because these methods yield a clear reduction in number of iterations.
Abstract: Most real world systems express themselves formally
as a set of nonlinear algebraic equations. As applications grow, the
size and complexity of these equations also increase. In this work, we
highlight the key concepts in using the homotopy analysis method
as a methodology used to construct efficient iteration formulas for
nonlinear equations solving. The proposed method is experimentally
characterized according to a set of determined parameters which
affect the systems. The experimental results show the potential and
limitations of the new method and imply directions for future work.
Abstract: In this paper, different approaches to solve the
forward kinematics of a three DOF actuator redundant hydraulic
parallel manipulator are presented. On the contrary to series
manipulators, the forward kinematic map of parallel manipulators
involves highly coupled nonlinear equations, which are almost
impossible to solve analytically. The proposed methods are using
neural networks identification with different structures to solve the
problem. The accuracy of the results of each method is analyzed in
detail and the advantages and the disadvantages of them in
computing the forward kinematic map of the given mechanism is
discussed in detail. It is concluded that ANFIS presents the best
performance compared to MLP, RBF and PNN networks in this
particular application.
Abstract: Phase-Contrast MR imaging methods are widely used
for measurement of blood flow velocity components. Also there are
some other tools such as CT and Ultrasound for velocity map
detection in intravascular studies. These data are used in deriving
flow characteristics. Some clinical applications are investigated
which use pressure distribution in diagnosis of intravascular disorders
such as vascular stenosis. In this paper an approach to the problem of
measurement of intravascular pressure field by using velocity field
obtained from flow images is proposed. The method presented in this
paper uses an algorithm to calculate nonlinear equations of Navier-
Stokes, assuming blood as an incompressible and Newtonian fluid.
Flow images usually suffer the lack of spatial resolution. Our
attempt is to consider the effect of spatial resolution on the pressure
distribution estimated from this method. In order to achieve this aim,
velocity map of a numerical phantom is derived at six different
spatial resolutions. To determine the effects of vascular stenoses on
pressure distribution, a stenotic phantom geometry is considered. A
comparison between the pressure distribution obtained from the
phantom and the pressure resulted from the algorithm is presented. In
this regard we also compared the effects of collocated and staggered
computational grids on the pressure distribution resulted from this
algorithm.