QA167 : The Non-Linear Superposition Principle And The Wei-Norman Method
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2013
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Abstarct: In this thesis we try to express a general method for finding the solutions of differential
equations by using the non-linear superposition principle and the Wei-Norman method and
their usage in differential equations. In Chapter 1, we explain the concepts and basic definitions that are needed. In chapter 2, first we state the definitions of prolongation and then
the prolongation of vector fields and group action are described with some examples. Other
sections of this chapter include differential invariants definition and some methods for calculating. In chapter 3,we review the problem of reducing a second order linear differential
equation to a non-linear Riccati differential equation. In the other sections of this chapter we
explain a method developed by Wei and Norman for determining the solutions of a differential
equations and we apply the method to study Riccati differential equation. The superposition
principle for first order differential equations system is studied in chapter 4.
Keywords:
#Non-Linear Superposition Principle #Riccati Differential Equations #Differential Equations #Symmetry of Differential Equations #Wei-Norman Method Link
Keeping place: Central Library of Shahrood University
Visitor:
Keeping place: Central Library of Shahrood University
Visitor: