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Stability of Spurious Period Two Solutions of Linear Theta-method

Liqiang Fan

Abstract



It is well-known that the discrete map can converge to a spurious steady state, many examples of such spurious behavior have been constructed. Stability of spurious period two solutions of linear theta method for ordinary differential equations have been examined. This paper focuses on the stability of spurious period two solutions of linear theta method for delay differential equations. Consider the two-stage theta-method applies to the scalar delay differential equation, the results that a period two solution is stable or unstable on different conditions are given. Some numerical examples demonstrate the results.

Keywords


dynamical system, linear theta method, spurious period two solution.

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