Numerical treatment of oscillatory functional differential equations
نویسندگان
چکیده
In this paper we are concerned with oscillatory functional differential equations (that is, those equations where all solutions oscillate) under numerical approximation. Our interest is in the preservation of qualitative properties of solutions under 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.
منابع مشابه
Parametric study of a novel oscillatory wind turbine
Clean energy harvesting and usage has gained considerable attention in the last few decades. While the horizontal axis wind turbines have been used extensively, they have certain defects and functional limitations. In the present paper, a novel oscillatory wind turbine is proposed. The conceptual design of the new turbine together with its configuration is explained. Dynamical equations of the ...
متن کاملNumerical solution of functional integral equations by using B-splines
This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.
متن کاملNumerical Treatment of Geodesic Differential Equations on Two Dimensional Surfaces
This paper presents a brief instructions to nd geodesics equa-tions on two dimensional surfaces in R3. The resulting geodesic equations are solved numerically using Computer Program Matlab, the geodesics are dis-played through Figures.
متن کاملAnalytical and numerical treatment of oscillatory mixed differential equations with differentiable delays and advances
In this work we study the oscillatory behaviour of the differential equation of mixed type x′ (t) = ∫ 0 −1 x (t− r (θ)) dν (θ) + ∫ 0 −1 x (t+ τ (θ)) dη (θ) with delays, r (θ) , and advances, τ (θ) , both differentiable. Some analytical and numerical criteria are obtained in order to guarantee that all solutions are oscillatory.
متن کاملOn the numerical analysis of rapid oscillation
This paper surveys recent advances in the allied challenges of discretizing highly oscillatory ordinary differential equations and computing numerical quadrature of highly oscillatory integrals, and attempts to sketch the mathematical foundations of a general approach to these issues. Having described the Magnus, Cayley and Neumann methods for highly oscillatory ordinary differential equations ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Computational Applied Mathematics
دوره 234 شماره
صفحات -
تاریخ انتشار 2010