𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Runge–Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

✍ Scribed by Z.W. Yang; M.Z. Liu; Juan J. Nieto

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
772 KB
Volume
233
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

Green's function Comparison theorems a b s t r a c t

In this paper we deal with the numerical solutions of Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green's function. It is shown that Runge-Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.

📜 SIMILAR VOLUMES

Stability of Runge–Kutta methods for the
Stability of Runge–Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments
✍ W.J. Lv; Z.W. Yang; M.Z. Liu 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 640 KB

This paper deals with the numerical properties of Runge-Kutta methods for the solution of u (t) = au(t) + a 0 u([t + 1 2 ]). It is shown that the Runge-Kutta method can preserve the convergence order. The necessary and sufficient conditions under which the analytical stability region is contained in

Weak first- or second-order implicit Run
Weak first- or second-order implicit Runge–Kutta methods for stochastic differential equations with a scalar Wiener process
✍ Yoshio Komori 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 363 KB

New fully implicit stochastic Runge-Kutta schemes of weak order 1 or 2 are proposed for stochastic differential equations with sufficiently smooth drift and diffusion coefficients and a scalar Wiener process, which are derivative-free and which are A-stable in mean square for a linear test equation