TY - JOUR
TI - Application of the heat-balance and refined integral methods to the Korteweg-de Vries equation
AU - Myers Timothy G
AU - Mitchell Sarah L
JN - Thermal Science
PY - 2009
VL - 13
IS - 2
SP - 113
EP - 119
PT - Article
AB - 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.