Two efficient methods for solving Schlömilch’s integral equation  

作　　者：Majeed Ahmed AL-Jawary Ghassan Hasan Radhi Jure Ravnik 

机构地区：[1]Department of Mathematics,College of Education for Pure Science/Ibn AL-Haitham,University of Baghdad,Baghdad,Iraq [2]Faculty of Mechanical Engineering,University of Maribor,Maribor,Slovenia

出　　处：《International Journal of Intelligent Computing and Cybernetics》2017年第3期287-309,共23页智能计算与控制论国际期刊（英文）

摘　　要：Purpose–In this paper,the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods.The Schlömilch’s integral equations have many applications in atmospheric,terrestrial physics and ionospheric problems.They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations.The paper aims to discuss these issues.Design/methodology/approach–First,the authors apply a regularization method combined with the standard homotopy analysis method to find the exact solutions for all forms of the Schlömilch’s integral equation.Second,the authors implement the regularization method with the variational iteration method for the same purpose.The effectiveness of the regularization-Homotopy method and the regularizationvariational method is shown by using them for several illustrative examples,which have been solved by other authors using the so-called regularization-Adomian method.Findings–The implementation of the two methods demonstrates the usefulness in finding exact solutions.Practical implications–The authors have applied the developed methodology to the solution of the Rayleigh equation,which is an important equation in fluid dynamics and has a variety of applications in different fields of science and engineering.These include the analysis of batch distillation in chemistry,scattering of electromagnetic waves in physics,isotopic data in contaminant hydrogeology and others.Originality/value–In this paper,two reliable methods have been implemented to solve several examples,where those examples represent the main types of the Schlömilch’s integral models.Each method has been accompanied with the use of the regularization method.This process constructs an efficient dealing to get the exact solutions of the linear and non-linear Schlömilch’s integral equation which is easy to implement.In addition to that,the accompanied regulariz

关 键 词：REGULARIZATION Homotopy analysis method Schlömilch’s integral equation Variational iteration method 

分 类 号：O17[理学—数学]