Graduation Term
3-30-2021
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Department of Mathematics
Committee Chair
George Seelinger
Abstract
Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.
Recommended Citation
Amangeldi, Medeu, "Lie Groups and Euler-Bernoulli Beam Equation" (2021). Theses and Dissertations. 1349.
https://ir.library.illinoisstate.edu/etd/1349
DOI
https://doi.org/10.30707/ETD2021.20210719070603170105.99
Page Count
64