4 papers · 1 filter
Explicit Runge-Kutta-Chebyshev methods of second order with monotonic stability polynomial
Boris Faleichik, Andrew Moisa
A new Chebyshev-type family of stabilized explicit methods for solving mildly stiff ODEs is presented. Besides conventional conditions of order and stability we impose an additiona…
Second order stabilized two-step Runge-Kutta methods
Andrew Moisa, Boris Faleichik
Stabilized methods (also called Chebyshev methods) are explicit methods with extended stability domains along the negative real axis. These methods are intended for large mildly st…
Stabilized explicit Adams-type methods
Vasily Repnikov, Boris Faleichik, Andrey Moysa
In this work we present explicit Adams-type multistep methods with extended stability interval, which are analogous to the stabilized Chebyshev Runge--Kutta methods. It is proved t…
Minimal residual multistep methods for large stiff non-autonomous linear problems
Boris Faleichik
The purpose of this work is to introduce a new idea of how to avoid the factorization of large matrices during the solution of stiff systems of ODEs. Starting from the general form…