Weak first- or second-order implicit Runge–Kutta methods for stochastic differential equations with a scalar Wiener process

✍ Scribed by Yoshio Komori

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 363 KB
• Volume: 217
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.06.024

✦ Synopsis

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 in some general settings. They are sought in a transparent way and their convergence order and stability properties are confirmed in numerical experiments.