Numerical treatment of oscillatory functional differential equations - Ford, Neville J.; Yan, Yubin; Abdul Malique, Md (Journal of computational and applied mathematics, 2010)
In this paper we are concerned with oscillatory functional differential equations (that is, those equations where all the solutions oscillate) under a numerical approximation. Our interest is in the preservation of qualitative properties of solutions under a numerical discretisation. We give conditions under which an equation is oscillatory, and consider whether the discrete schemes derived using linear ϑ -methods will also be oscillatory. We conclude with some general theory.