Novel phase-fitted symmetric splitting methods for chemical oscillators

Splitting strategy is considered for the numerical solution of oscillatory chemical reaction systems. When applied to the harmonic oscillator, traditional splitting methods with constant coefficients are shown to be have some order of phase lag though they are zero-dissipative. Phase-fitted symmetric splitting methods of order two and order four are constructed. The result of the numerical experiment on the Lotka–Volterra system shows that the new phase-fitted symmetric splitting methods are more effective than their prototype splitting methods and can preserve the invariant of the system in long-term compared with the classical Runge–Kutta method.