Almost periodic type solutions of some differential equations with piecewise constant argument
Nonlinear Analysis: Theory, Methods & Applications
Stability of Runge--Kutta methods in the numerical solution of equation u'(t) = au(t) + a0u([t])
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Preservation of oscillations of the Runge-Kutta method for equation x'(t)+ax(t)+a1x([t-1])=0
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Stability of θ-methods for advanced differential equations with piecewise continuous arguments
Computers & Mathematics with Applications
Hi-index | 7.29 |
This paper is concerned with the numerical properties of @q-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two @q-methods, namely the one-leg @q-method and the linear @q-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the @q-methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the @q-methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results.