APPLICATION OF THE HEAT-BALANCE AND REFINED INTEGRAL METHODS TO THE KORTEWEG-DE VRIES EQUATION

Abstract

In this paper we consider approximate travelling wave solutions to the Korteweg-de Vries equation. The heat-balance integral method is first applied to the problem, using two different quartic approximating functions, and then the refined integral method is investigated. We examine two types of solution, chosen by matching the wave speed to that of the exact solution and by imposing the same area. The first set of solutions is generally better with an error that is fixed in time. The second set of solutions has an error that grows with time. This is shown to be due to slight discrepancies in the wave speed.

Keywords

Dates

  • Submission Date2008-05-28
  • Revision Date2008-06-20
  • Acceptance Date2008-09-25

DOI Reference

10.2298/TSCI0902113M

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Volume 13, Issue 2, Pages113 -119