In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.
Summary
I wanted to address this topic because of creedal purposes importance,and its r le in regulating lives of individuals and society, and to talk about purposes of Almighty's saying:{It is easy for me},to simplify its meanings for general educated person to obtain the believe of the Creator’s power and his oneness.
Therefore,this research came,whichincludes:an introduction and topics, first :concept of creedal objectives and their divisions,second: creedal purposes in Almighty’s saying:{It is easy for me},and conclusion:in where most important results were included:
... Show MoreIn this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using
In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met
... Show MoreIn this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using
A simple, fast, selective of a new flow injection analysis method coupled with potentiometric detection was used to determine vitamin B1 in pharmaceutical formulations via the prepared new selective membranes. Two electrodes were constructed for the determination of vitamin B1 based on the ion-pair vitamin B1-phosphotungestic acid (B1-PTA) in a poly (vinyl chloride) supported with a plasticized di-butyl phthalate (DBPH) and di-butyl phosphate (DBP). Applications of these ion selective electrodes for the determination of vitamin B1 in the pharmaceutical preparations for batch and flow injection systems were described. The ion selective membrane exhibited a near-Nernstian slope values 56.88 and 58.53 mV / decade, with the linear dy
... Show MoreInfertility can be detected when the couples have not completed pregnancy after a year or more of normal coitus. So, in order to treat infertility, there are many supported reproductive techniques are in practice. The success rate of these techniques depends upon the way by which preparation of the paternal semen sample. Over the past 30 years, the manual has been standard as providing global standards and has been used extensively by research and clinical laboratories throughout the world. The spermatozoa of all placental (eutherian) mammals, including humans, are in a protective, no labile formal at ejaculation and are incapable of fertilization even if they are placed in direct contact with an oocyte. Accordingly, they must undergo a sub
... Show MoreGreenhouses are provide that produce of vegetable in non times seasons production by controlling the various environmental factors that appropriate atmosphere in temperature and humidity for the growth of plants in the plastic houses and owner plastic.
The objective of this research is to study of the most important natural and human factors affecting the Greenhouses in the province of Baghdad and study geographic distribution for the Greenhouses in the province.
Some properties on curriculum geographical descriptive analytical that used in describe and analysis of data and information that could be available from Directorate of agriculture in Baghdad to 2014. As it turns out that district of Mahmudiya acquired (45.3%) of the total
The research Was based to on a real problem and realistically of represented by that Iraqi Airways company does not have the electronic cost accounting system and therefore be the process of the pricing various services provided by a company sample research respecting air transport and air cargo and aviation fuel and services and catering are not properly especially in the presence of new data from the new companies entering competition in Iraqi aviation industry and therefore does not provide price flexibility in order to compete in getting market share, And then research this problem addressed through design an electronic cost Accounting system covers all the costs incurred by the compan
... Show MoreThe tight gas is one of the main types of the unconventional gas. Typically the tight gas reservoirs consist of highly heterogeneous low permeability reservoir. The economic evaluation for the production from tight gas production is very challenging task because of prevailing uncertainties associated with key reservoir properties, such as porosity, permeability as well as drainage boundary. However one of the important parameters requiring in this economic evaluation is the equivalent drainage area of the well, which relates the actual volume of fluids (e.g gas) produced or withdrawn from the reservoir at a certain moment that changes with time. It is difficult to predict this equival