From Nonlinear to Linear Differential Equations using Transformation Groups

R. Seshadri and T. Y. Na
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R. Seshadri: Syncrude Canada Limited
T. Y. Na: University of Michigan—Dearborn, Department of Mechanical Engineering

Chapter Chapter 10 in Group Invariance in Engineering Boundary Value Problems, 1985, pp 169-189 from Springer

Abstract: Abstract The mathematical descriptions of large number of physical problems arising in science and engineering manifest themselves as nonlinear differential equations. Since there is an abundance of methods for dealing with linear differential equations, a popular practice has been to introduce some form of approximation that would linearize the nonlinear equation. These approximations usually impose certain restrictions on the solutions. In this chapter, we will discuss procedures for deriving mappings based on group- theoretic motivations that transform a nonlinear differential equation into a linear differential equation.

Keywords: Group Method; Nonlinear Differential Equation; Linear Differential Equation; Trial Mapping; Nonlinear Partial Differential Equation (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5102-6_10

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DOI: 10.1007/978-1-4612-5102-6_10

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