Higher order dispersive and dissipative hybrid method for the numerical solution of oscillatory problems

Abstract

In this paper, an improved explicit two-step hybrid method with fifth algebraic order is derived. The new method possesses dispersion of order 10 and dissipation of order seven, which is first of its kind in the literature. Numerical experiment reveals the superiority of the new method for solving oscillatory or periodic problems over several methods of the same algebraic order.

Keywords:

• oscillatory solution
• dispersion
• dissipation
• hybrid method
• initial value problem
• oscillatory problem

C.R Categories:

• G1.7

2010 AMS Subject Classification:

• 65L05

Disclosure statement

No potential conflict of interest was reported by the authors.