Non-dissipative extended one-step methods for oscillatory problems

Abstract

We examine stability of the class of extended one-step methods introduced in Chawla et al. [6] for the numerical integration of first-order initial-value problems y′ = f(t,y)y (t ₀) = η, which possess oscillating solutions. We first characterize those methods which are non-dissipative for the integration of problems with oscillating solutions, and then derive non-dissipative methods of orders two to five. Interestingly, a modified version of Simpson's rule is shown to be non-dissipative for the integration of oscillatory problems. The obtained methods are numerically tested on problems taken from real-world applications.

Keywords:

• Initial-value problem
• ordinary differential equations
• oscillating solutions
• extended one-step methods
• non-dissipative methods
• Simpson's rule
• Lorenz system
• Van der Pol oscillator
• predator-prey oscillations

C.R. Categories:

• G.1.7

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^*Corresponding author.

Notes

^*Corresponding author.