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From Nonlinear to Linear Differential Equations using Transformation Groups

In: Group Invariance in Engineering Boundary Value Problems

Author

Listed:
  • R. Seshadri

    (Syncrude Canada Limited)

  • T. Y. Na

    (University of Michigan—Dearborn, Department of Mechanical Engineering)

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.

Suggested Citation

  • R. Seshadri & T. Y. Na, 1985. "From Nonlinear to Linear Differential Equations using Transformation Groups," Springer Books, in: Group Invariance in Engineering Boundary Value Problems, chapter 0, pages 169-189, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5102-6_10
    DOI: 10.1007/978-1-4612-5102-6_10
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