Weak Order Implicit Stochastic Runge-Kutta Methods for Stochastic Differential Equations with a Scalar Wiener Process

New implicit stochastic Runge-Kutta schemes of weak order 1 or 2 are proposed for stochastic differential equations with a scalar Wiener process, which are derivativefree, which attain order 2 or 4 for ordinary differential equations, 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