Methods of Variations and Their Applications  

作　　者：Arij A. Awin Ahlam A. Elasheq Abdulmtalb M. Hussen Ali M. Awin Arij A. Awin;Ahlam A. Elasheq;Abdulmtalb M. Hussen;Ali M. Awin(Department of Mathematics, College of Science, University of Tripoli, Tripoli, Libya;Department of Mathematics, Navajo Technical University, New Mexico, USA)

机构地区：[1]Department of Mathematics, College of Science, University of Tripoli, Tripoli, Libya [2]Department of Mathematics, Navajo Technical University, New Mexico, USA

出　　处：《Journal of Applied Mathematics and Physics》2023年第5期1263-1286,共24页应用数学与应用物理（英文）

摘　　要：In this review article, we begin with reviewing Calculus of variations giving few examples on its use to solve a large number of problems in geometry, physics, and other branches of knowledge. Afterwards, we direct our attention to different methods of variations which evolved during the last century and which include their use in eigenvalue problems and in finite difference methods and those adopted in classical and quantum mechanics. The methods used in evaluating products and quotients of functionals are also discussed along with variational iteration methods. Later on, a good number of applications in different areas are presented and discussed;then a concluding discussion is given.In this review article, we begin with reviewing Calculus of variations giving few examples on its use to solve a large number of problems in geometry, physics, and other branches of knowledge. Afterwards, we direct our attention to different methods of variations which evolved during the last century and which include their use in eigenvalue problems and in finite difference methods and those adopted in classical and quantum mechanics. The methods used in evaluating products and quotients of functionals are also discussed along with variational iteration methods. Later on, a good number of applications in different areas are presented and discussed;then a concluding discussion is given.

关 键 词：VARIATION ITERATION CALCULUS Method APPLICATIONS Technique EXTREME 

分 类 号：O17[理学—数学]