Author(s)

Arij A. Awin¹, Ahlam A. Elasheq¹, Abdulmtalb M. Hussen², Ali M. Awin¹

¹Department of Mathematics, College of Science, University of Tripoli, Tripoli, Libya.
²Department of Mathematics, Navajo Technical University, New Mexico, USA.

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.

Variation, Iteration, Calculus, Method, Applications, Technique, Extreme

Awin, A. , Elasheq, A. , Hussen, A. and Awin, A. (2023) Methods of Variations and Their Applications. Journal of Applied Mathematics and Physics, 11, 1263-1286. doi: 10.4236/jamp.2023.115082.