Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

L1 adaptive controller has proven to provide fast adaptation with guaranteed transients in a large variety of systems. It is commonly used for controlling systems with uncertain time-varying unknown parameters. The effectiveness of  L1 adaptive controller for position control of single axis has been examined and compared with Model Reference Adaptive Controller (MRAC). The Linear servo motor is one of the main constituting elements of the x-y table which is mostly used in automation application. It is characterized by time-varying friction and disturbance.

    The tracking and steady state performances of both controllers have been assessed fo

In this paper, a robust adaptive sliding mode controller is designed for a mobile platform trajectory tracking.  The mobile platform is an example of a nonholonomic mechanical system. The presence of holonomic constraints reduces the number of degree of freedom that represents the system model, while the nonholonomic constraints reduce the differentiable degree of freedom. The mathematical model was derived here for the mobile platform, considering the existence of one holonomic and two nonholonomic constraints imposed on system dynamics. The partial feedback linearization method was used to get the input-output relation, where the output is the error functions between the position of a certain point on the platform

In this paper, a self-tuning adaptive neural controller strategy for unknown nonlinear system is presented. The system considered is described by an unknown NARMA-L2 model and a feedforward neural network is used to learn the model with two stages. The first stage is learned off-line with two configuration serial-parallel model & parallel model to ensure that model output is equal to actual output of the system & to find the jacobain of the system. Which appears to be of critical importance parameter as it is used for the feedback controller and the second stage is learned on-line to modify the weights of the model in order to control the variable parameters that will occur to the system. A back propagation neural network is appl

This paper addresses the use of adaptive sliding mode control for the servo actuator system with friction. The adaptive sliding mode control has several advantages over traditional sliding mode control method. Firstly, the magnitude of control effort is reduced to the minimal admissible level defined by the conditions for the sliding mode to exist. Secondly, the upper bounds of uncertainties are not required to be known in advance. Therefore, adaptive sliding mode control method can be effectively implemented. The numerical simulation via MATLAB 2014a for servo actuator system with friction is investigated to confirm the effectiveness of the proposed robust adaptive sliding mode control scheme. The results clarify, after

The hydraulic conditions of a flow previously proved to be changed when placing large-scale geometric roughness elements on the bed of an open channel. These elements impose more resistance to the flow.  The geometry of the roughness elements, the numbers used, and the configuration are parameters that can affect the hydraulic flow characteristics. The target is to use inclined block elements to control the salt wedge propagation pointed in most estuaries to prevent its negative effects. The Computational Fluid Dynamics CFD Software was used to simulate the two-phase flow in an estuary model. In this model, the used block elements are 2 cm by 3 cm cross-sections with an inclined face in the flow direction, with a length

Surface drip irrigation is one of the most conservative irrigation techniques that help control providing water directly on the soil through the emitters. It can supply fertilizer and providing water directly to plant roots by drippers. One of the essential needs for trickle irrigation nowadays is to obtain more knowledge about the moisture pattern under the trickling source for various types of soil with various discharge levels with trickle irrigation. Simulation numerical using HYDRUS-2D software, version 2.04 was used to estimate an equation for the wetted area from a single surface drip irrigation in unsaturated soil is taking into account water uptake by roots. In this paper, using two soil types were used, namely