Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries

O. O. Vaneeva, N. C. Papanicolaou, M. A. Christou, C. Sophocleous

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary value problem for certain subclasses of the above class. Namely, the found Lie symmetries are applied in order to reduce the initial and boundary value problem for the generalized KdV equations (which are PDEs) to an initial value problem for nonlinear third-order ODEs. The latter problem is solved numerically using the finite difference method. Numerical solutions are computed and the vast parameter space is studied.

Original languageEnglish
Pages (from-to)3074-3085
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume19
Issue number9
DOIs
Publication statusPublished - 2014

Keywords

  • Boundary value problems
  • Equivalence transformations
  • KdV equations
  • Lie symmetries
  • Numerical solutions

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