In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

Abstract

Electric arc furnace applications in industry are related to position system of its pole, up and down of pole. The pole should be set the certain gap. These setting are needed to calibrate. It is done manually. In this research will proposed smart hydraulic to make this pole works as intelligent using proportional directional control valve. The output of this research will develop and improve the working of the electric arc furnace. This research requires study and design of the system to achieve the purpose and representation using Automation Studio software (AS), in addition to mathematically analyzed and where they were building a laboratory device similar to the design and conduct experiments to stud

Solar energy is one of the immeasurable renewable energy in power generation for a green, clean and healthier environment. The silicon-layer solar panels absorb sun energy and converts it into electricity by off-grid inverter. Electricity is transferred either from this inverter or from transformer, consumed by consumption unit(s) available for residential or economic purposes. The artificial neural network is the foundation of artificial intelligence and solves many complex problems which are difficult by statistical methods or by humans. In view of this, the purpose of this work is to assess the performance of the Solar - Transformer - Consumption (STC) system. The system may be in complete breakdown situation due to failure of both so

An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has

     In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.

Presents here in the results of comparison between the theoretical equation stated by Huang and Menq and laboratory model tests used to study the bearing capacity of square footing on geogrid-reinforced loose sand by performing model tests. The effects of several parameters were studied in order to study the general behavior of improving the soil by using the geogrid. These parameters include depth of first layer of reinforcement, vertical spacing of reinforcement layers, number of reinforcement layers and types of reinforcement layers The results show that the theoretical equation can be used to estimate the bearing capacity of loose sand.